Section 3.1  Pythagoras' Theorem 
Question 1
Which side is the HYPOTENUSE in the diagram below?

(A)  XY 

 
(B)  YZ 
(C)  XZ 
(D)  None of these 

Question 2
Which side is the HYPOTENUSE in the diagram below?

(A)  XY 

 
(B)  YZ 
(C)  XZ 
(D)  None of these 
 
Question 3
Which of the following sets of numbers are Pythagorean triples
(that is, a^{2} + b^{2} =
c^{2})?
1. 3, 4, 5
2. 5, 6, 7
3. 6, 8, 10 
(A)  1 only 


(B)  1 and 2 only 
(C)  1 and 3 only 
(D)  2 and 3 only 

Question 4
What value of x satisfies x^{2} =
9^{2} + 12^{2}? 
(A)  15 


(B)  18 
(C)  21 
(D)  None of these 
 
Section 3.2  Calculating the Length of the Hypotenuse 
Question 5
What is the length of the hypotenuse in the triangle below?

(A)  13 cm 


(B)  15 cm 
(C)  17 cm 
(D)  None of these 

Question 6
What is the length of the hypotenuse in the triangle below?
Give your answer correct to 1 decimal place.

(A)  8.0 cm 


(B)  9.2 cm 
(C)  9.3 cm 
(D)  10.0 cm 

Question 7
What is the length of the diagonals of a square of side 6 cm?
Give your answer correct to 1 decimal place. 
(A)  8.4 cm 


(B)  8.5 cm 
(C)  8.6 cm 
(D)  12.0 cm 

Question 8
What is the length of the diagonal of the rectangle below?
Give your answer correct to 1 decimal place.

(A)  10.0 cm 


(B)  5.0 cm 
(C)  3.6 cm 
(D)  3.5 cm 

Section 3.3  Calculating the Lengths of Other Sides 
Question 9
What is the length of the side marked x in the triangle below?
Give your answers correct to 1 decimal place.

(A)  13.2 cm 


(B)  13.3 cm 
(C)  25.0 cm 
(D)  None of these 

Question 10
What is the length of the side marked x in the triangle below?
Give your answers correct to 1 decimal place.

(A)  3.0 cm 


(B)  7.9 cm 
(C)  9.0 cm 
(D)  None of these 

Question 11
What is the perpendicular height of the isosceles triangle shown below?
Give your answer correct to 1 decimal place.

(A)  6.5 cm 


(B)  6.6 cm 
(C)  6.7 cm 
(D)  7.4 cm 

Question 12
What is the perpendicular height of an equilateral triangle with sides of length 6 cm?
Give your answer to 1 decimal place. 
(A)  5.1 cm 


(B)  5.2 cm 
(C)  5.5 cm 
(D)  6.7 cm 

Section 3.4  Problems in Context 
Question 13
A ship sails 200 km due east and then 100 km due north.
At the end of this journey, how far is the ship from its starting position?
Give your answer to the nearest 10 km. 
(A)  170 km 


(B)  200 km 
(C)  220 km 
(D)  None of these 

Question 14
What is the area of the triangle shown below?

(A)  42 cm^{2} 


(B)  67.5 cm^{2} 
(C)  84 cm^{2} 
(D)  None of these 

Question 15
What is the perimeter of the triangle shown below?

(A)  30 cm 


(B)  34 cm 
(C)  60 cm 
(D)  None of these 

Question 16
What is the perimeter of the parallelogram shown below?
Give your answer to the nearest millimetre.

(A)  20.0 cm 


(B)  20.9 cm 
(C)  21.0 cm 
(D)  None of these 
