Work out the length of the hypotenuse of a right-angled triangle with legs 3 cm and 4 cm.
(Total for Question 1 is 1 mark)
2
A right triangle has hypotenuse 13 m and one shorter side 5 m. Work out the length of the other shorter side.
(Total for Question 2 is 2 marks)
3
Work out the hypotenuse of a right triangle with legs 7 cm and 24 cm.
(Total for Question 3 is 2 marks)
4
A rectangle measures 6 m by 8 m. Work out the length of the diagonal of the rectangle.
(Total for Question 4 is 2 marks)
5
A ladder of length 5.0 m leans against a wall and reaches 4.0 m up the wall. Work out the distance from the foot of the ladder to the wall. Give your answer in metres.
(Total for Question 5 is 2 marks)
6
A triangle has sides 8 cm, 15 cm and 17 cm. Is this triangle right-angled? Give a reason for your answer.
(Total for Question 6 is 2 marks)
7
A square garden has side length 9.0 m. Work out the length of the diagonal of the garden. Give your answer to 1 decimal place.
(Total for Question 7 is 3 marks)
8
A right-angled triangle has hypotenuse 20 cm and one shorter side 12 cm. Work out the length of the other shorter side.
(Total for Question 8 is 2 marks)
9
Find the area of a right-angled triangle with shorter sides 9 cm and 12 cm.
(Total for Question 9 is 2 marks)
10
A square carpet has diagonal length 5.0 m. Work out the length of one side of the carpet. Give your answer to 2 decimal places.
(Total for Question 10 is 3 marks)
11
Work out the hypotenuse of a right triangle with legs 14 m and 48 m.
(Total for Question 11 is 2 marks)
12
A right triangle has hypotenuse 25 cm and one shorter side 7 cm. Work out the length of the other shorter side.
(Total for Question 12 is 2 marks)
13
On a grid a point A is at (2, 3) and a point B is at (8, 11). Work out the straight-line distance AB. Give your answer in whole numbers if appropriate.
(Total for Question 13 is 2 marks)
14
Find the area of a right-angled triangle with shorter sides 5 cm and 12 cm.
(Total for Question 14 is 2 marks)
15
A right-angled isosceles triangle has equal shorter sides 6.0 m and 6.0 m. Work out the length of the hypotenuse. Give your answer to 1 decimal place.
(Total for Question 15 is 2 marks)
16
A ramp rises 1.20 m from the ground to a doorway and the base of the ramp is 4.00 m from the doorway. Find the length of the ramp. Give your answer to 2 decimal places.
(Total for Question 16 is 3 marks)
Mark scheme · 4.9F Pythagoras: Foundation Tier Practice
Question 1
B1 5 cm cao
Answer: 5 cm
Question 2
M1 use method: other2 = 132 - 52 or show 169 - 25
A1 12 m cao
Answer: 12 m
Question 3
M1 use method: hyp2 = 72 + 242 or show 49 + 576
A1 25 cm cao
Answer: 25 cm
Question 4
M1 use method: diagonal2 = 62 + 82 or show 36 + 64
A1 10 m cao
Answer: 10 m
Question 5
M1 use method: base2 = 5.02 - 4.02 or show 25 - 16
A1 3.0 m cao
Answer: 3.0 m
Question 6
B1 Yes, because 82 + 152 = 64 + 225 = 289 which equals 172
B1 reason stated that square of longest side equals sum of squares of other two sides oe
Answer: Yes. 82 + 152 = 172 (64 + 225 = 289), so it is right-angled.
Question 7
M1 use method: diagonal2 = 9.02 + 9.02 or show 81 + 81
M1 calculate diagonal = √162 with a calculator
A1 12.7 m awrt
Answer: 12.7 m
Question 8
M1 use method: other2 = 202 - 122 or show 400 - 144
A1 16 cm cao
Answer: 16 cm
Question 9
M1 use method: area = 1/2 * 9 * 12 or show 0.5 * 9 * 12
A1 54 cm2 cao
Answer: 54 cm2
Question 10
M1 use method: side2 + side2 = 5.02 or 2*side2 = 25
M1 calculate side = √25/2
A1 3.54 m awrt
Answer: 3.54 m
Question 11
M1 use method: hyp2 = 142 + 482 or show 196 + 2304
A1 50 m cao
Answer: 50 m
Question 12
M1 use method: other2 = 252 - 72 or show 625 - 49
A1 24 cm cao
Answer: 24 cm
Question 13
M1 use method: difference in x = 6, difference in y = 8, distance = √62 + 82
A1 10 units cao
Answer: 10 units
Question 14
M1 use method: area = 1/2 * 5 * 12
A1 30 cm2 cao
Answer: 30 cm2
Question 15
M1 use method: hyp2 = 6.02 + 6.02 or show 36 + 36
A1 8.5 m awrt
Answer: 8.5 m
Question 16
M1 use method: length2 = 1.202 + 4.002 or show 1.44 + 16.00