Robinson Tuition
Grade 5 · Foundation and Higher · free GCSE maths worksheet

Pythagoras' theorem: finding a shorter side

Subtracting squares.

9 original questions, 27 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Triangle DEF is a right-angled triangle with the right angle at E.

The hypotenuse DF = 20 cm and DE = 8 cm.

Work out the length of EF.

Give your answer correct to 1 decimal place.

DEF8 cm20 cmDiagram NOT accurately drawn
2 marks
Show answer
18.3 cm
2

Triangle PQR has a right angle at Q. PR = 17 cm and PQ = 8 cm.

Work out the length of QR.

2 marks
Show answer
15 cm
3

A rectangular screen has a diagonal of 15 inches and a width of 9 inches.

Work out the height of the screen.

3 marks
Show answer
12 inches
4

A kite is flying on a straight string that is 45 m long. The kite is 28 m horizontally from the person holding the other end of the string. The person holds the string at ground level.

Work out the height of the kite above the ground. Give your answer correct to 1 decimal place.

3 marks
Show answer
35.2 m
5

A straight wheelchair ramp is 3.4 m long. It starts 3.2 m horizontally from the base of a platform and reaches the top of the platform.

Work out the height of the platform. Give your answer in metres, correct to 2 decimal places.

3 marks
Show answer
1.15 m
6

Triangle ABC has a right angle at B. AC = 9 cm and AB = 6 cm.

Work out the length of BC. Give your answer as a surd in its simplest form.

3 marks
Show answer
3 root 5 cm
7

An isosceles triangle has two equal sides of length 9 cm and a base of length 10 cm.

  1. Work out the perpendicular height of the triangle. Give your answer correct to 1 decimal place.
  2. Work out the area of the triangle. Give your answer correct to 1 decimal place.
4 marks
Show answer
a) 7.5 cm b) 37.4 cm2
8

A ladder is 6.5 m long.

The ladder leans against a vertical wall, with the foot of the ladder on horizontal ground 2.5 m from the base of the wall.

Work out how far up the wall the top of the ladder reaches.

6.5 m2.5 mwallgroundDiagram NOT accurately drawn
3 marks
Show answer
6 m
9

ABCD is a trapezium. AB is parallel to DC. The angles at A and D are both 90°.

AB = 9 cm, DC = 14 cm and BC = 13 cm.

Work out the area of the trapezium.

4 marks
Show answer
138 cm2

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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