Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Which of these numbers is a square number: 14, 49, 98, or 56?
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2.
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Which 2 consecutive square numbers is 54 between?
a. | 53 and 55 | b. | 28 and 32 | c. | 49 and 64 | d. | 12 and 16
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3.
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Find 82.
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4.
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Find the number whose square root is 36.
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5.
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Simplify 72.
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6.
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The area of a square is 8 m2. Find its side length.
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7.
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Copy each line segment on grid paper. Without measuring, determine which line
segment is shortest.  a. | Line A | b. | Line C | c. | Line B | d. | Line
D |
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8.
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What is the least whole number greater than  ?
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9.
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Find the approximate side length of a square with area 27 cm2.
Give your answer to 1 decimal place.
a. | 13.5 cm | b. | 6.8 cm | c. | 5.2 cm | d. | 3.7
cm |
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10.
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Find the length of the leg labelled r.
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11.
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Find the length of the diagonal, d, in the rectangle. Give your answer to
the nearest centimetre.  a. | 320 cm | b. | 18 cm | c. | 24 cm | d. | 14
cm |
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12.
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Use the Pythagorean Theorem to find the area of this square.  a. | 13 square units | b. | 16 square units | c. | 9 square units | d. | 2 square
units |
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13.
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The area, in square centimetres, of the square on each side of a triangle is
given. Which triangle is a right triangle?  a. | Triangle A | b. | Triangle B | c. | Triangle C | d. | Triangle
D |
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14.
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The area, in square centimetres, of the square on each side of a triangle is
given. Which triangle is NOT a right triangle?  a. | Triangle D | b. | Triangle C | c. | Triangle B | d. | Triangle
A |
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15.
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The legs of a right triangle measure 11 cm and 8 cm. What is the length of the
hypotenuse?
a. | 185 cm | b. |  cm | c. | 19 cm | d. | 361
cm |
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Short Answer
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16.
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Which of these numbers is a perfect square: 34, 36, 38, or
40?
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17.
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What is the area of this square? 
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18.
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The area of a square is 65 cm2. Find its side length.
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19.
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Copy the line segment on grid paper. Draw a square on the line
segment. Find the area of the square and the length of the line segment. 
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20.
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Is 5 greater than, less than, or equal to  ?
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21.
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A square patio covers one-quarter of the area of a garden. The garden is 36 m by
36 m.
What are the dimensions of the patio?
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22.
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Which has the longer diagonal, the rectangle or the square? 
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23.
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A square has area 169 cm2. Determine the length of the sides and the
length of the diagonal.
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24.
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Two numbers in a Pythagorean triple are given. Find the third number.
8,
15
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25.
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Is this set of numbers a Pythagorean triple? How do you know?
2, 21,
29
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26.
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Which 3 of these numbers form a Pythagorean triple?
7, 15, 24, 25
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27.
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Use these numbers to make sets of side lengths that form right triangles: 
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28.
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Determine whether a triangle with each set of side lengths is a right triangle.
a) 9 cm, 12, cm, 15
cm
b) 24 cm, 10 cm, 26 cm
c) 22 cm,
21, cm, 30 cm
d) 21 cm, 20 cm, 29 cm
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29.
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This logo is made up of 4 congruent right triangles. Find the perimeter of the
logo. 
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30.
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A boat sails due south from a port at a steady speed of 9 km/h.
The wind
blows the boat due west at a speed of 3 km/h.
How far is the boat from the port after 1 h?
Give your answer to 1 decimal place.
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Problem
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31.
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The numbers 2, 3, 5, 7, 11, and 13 are written on separate cards.
Which
pairs of numbers give a sum that is a perfect square?
Find all possible solutions.
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32.
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Use 1-cm grid paper. Draw as many different rectangles as you can with area
36 cm 2. Find the base and height of each rectangle. Record the results in a
table. Base
(cm) | Height
(cm) | Perimeter
(cm) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
Which rectangle has the least
perimeter? What can you say about this rectangle?
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33.
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Copy the square on grid paper. a) Find its
area. b) Then write the side length of the square. 
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34.
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Copy each square on grid paper. Find its area. Then write the side length
of each square. Explain your work. 
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35.
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a) Estimate each
square root to 2 decimal places.  ,  ,  ,
 ,  b) Look at your results in
part a. What patterns do you see?
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36.
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Which whole number is  closer to?
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37.
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In this diagram,  . Find the measure of ST. Show your work. Give your
answer to 1 decimal place. 
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38.
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Which sets of numbers are Pythagorean triples?
Show how you know.
a) 5, 12, 13
b)
26, 36, 45
c) 24, 70, 84
d) 57,
176, 185
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39.
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PQRS is a trapezoid with  . Find the length of RS. Give the length
to the nearest millimetre. Show your work. 
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40.
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At a water sports centre, 4 markers form a square with side length 90 m.
Evan kayaked from Start to Marker 1, then to Marker 2. From Marker 2 he kayaked straight back
to Start. How far, to the nearest metre, did he kayak? 
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