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Pythagoras' Theorem: Fluency and Exam Drill - Worksheets, Questions and Revision

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KS3 · Geometry and Measures

KS3.M-G14D Pythagoras' Theorem: Fluency and Exam Drill

AQA KS3.M-G14 · Calculators not allowed · about 50 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A right-angled triangle has short sides 20 cm and 21 cm. Work out the length of the hypotenuse.
(1)
2
A right-angled triangle has legs 12 cm and 35 cm. Give the length of the hypotenuse.
(1)
3
A right-angled triangle has hypotenuse 61 cm and one short side 11 cm. Find the length of the other short side.
(1)
4
A right-angled triangle has sides 28 cm and 45 cm. Work out the length of the hypotenuse.
(1)
5
A right-angled triangle has hypotenuse 65 cm and one short side 33 cm. Calculate the other short side.
(1)
6
A right-angled triangle has legs 16 cm and 63 cm. Work out the length of the hypotenuse.
(1)
7
A right-angled triangle has hypotenuse 85 cm and one short side 13 cm. Find the other short side.
(1)
8
A rectangular garden has length 77 m and width 36 m. Calculate the length of a diagonal path across the garden.
(2)
9
A right-angled triangle has one short side 39 cm and hypotenuse 89 cm. Find the length of the other short side.
(2)
10
A right-angled triangle has short sides 48 mm and 55 mm. Find the length of the hypotenuse.
(2)
11
A right-angled triangle has hypotenuse 97 cm and one short side 65 cm. Find the other short side.
(2)
12
A square has side length 12 cm. Calculate the length of its diagonal, giving your answer to 2 decimal places.
(2)
13
A ramp rises 2.4 m over a horizontal distance of 7 m. Calculate the length of the ramp.
(2)
14
A rectangular field has length 99 m and width 20 m. A farmer wants to walk diagonally across the field instead of along two sides. Calculate the length of the diagonal path.
(3)
15
A square has diagonal 20 cm. Find the length of each side, giving your answer to 2 decimal places.
(3)
16
A TV screen has width 84 cm and diagonal 91 cm. Calculate the height of the screen, giving your answer to 1 decimal place.
(3)
17
A triangular field is right-angled. One short side is 33 m and the hypotenuse is 65 m. A farmer wants to fence the two short sides only. Calculate the total length of fencing needed.
(3)
18
A ship sails 45 km due east from port P to point Q, then sails 28 km due north from Q to point R.
(a)Calculate the direct distance from P to R.(2)
(b)The ship then sails directly back from R to P at a speed of 13 km/h. Calculate how long the return journey takes, giving your answer in hours to 1 decimal place.(2)
19
A framework is in the shape of an isosceles triangle. The two equal sloping sides are each 37 cm long, and the base of the triangle is 24 cm.
(a)Find the height of the triangle (the perpendicular distance from the apex to the base).(2)
(b)Hence find the area of the triangle.(1)
(c)A second, similar triangular framework has all its side lengths exactly half those of the first. State its two equal side lengths and its base, and use Pythagoras' theorem directly on this smaller triangle to find its area.(2)
Mark scheme · KS3.M-G14D Pythagoras' Theorem: Fluency and Exam Drill

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