Length of a shorter side | Maths | Quizalize & Oak National Academy

Starter quiz

The triangle formed from these three squares is right-angled. Find the area of the square labelled $h$ units².

7.22

44

48.17

52 ✓

2320
The triangle formed from these three squares is right-angled. The area of the square labelled $p$ units² is ______ units².

'110' ✓
The area, $w$ , of the largest square in this diagram, is ______ cm².

'100' ✓
Find the length of the hypotenuse of this triangle.

5 cm

10 cm ✓

14 cm

50 cm

10 000 cm
The length of the hypotenuse for this triangle is ______ units.

'23' ✓
The length of the hypotenuse of this triangle is ______ cm.

'82' ✓

Exit quiz

Find the length of the shorter side of this right-angled triangle, labelled $b$ .

6.67 units

13 units ✓

16 units

169 units
The length of the shorter side of this right-angled triangle, labelled $c$ is ______ cm.

'17' ✓
The length of the shorter side of this right-angled triangle, labelled $d$ , is ______ cm, rounded to 2 decimal places.

'8.77' ✓
The length of the side $x$ cm is ______ cm, rounded to 2 decimal places.

'10.58' ✓
A right-angled triangle has a hypotenuse of 130 cm. The length of one of its shorter sides is 66 cm. Using Pythagoras' theorem, the perimeter of this triangle is ______ cm.

'308' ✓
Calculate the area of this right-angled triangle.

112 cm²

840 cm² ✓

847.5 cm²

1680 cm²

1695 cm²

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

The sum of the squares of the two shorter sides equals the square of the longest side.
The difference between the squares of the longest and known shorter sides is the square of the remaining side.
A calculator can perform these calculations efficiently.
Rounding gives a less accurate answer so there might be times you wish to leave your answer with an operator.

Common misconception

The method for finding the length of a shorter side of a right-angled triangle using Pythagoras' theorem is exactly the same as when finding the hypotenuse.

Whilst the initial setup of "the sum of the squares of the two shorter sides equals the square of the hypotenuse" will be the same, finding the length of a shorter side will require an extra step of rearranging terms in the equation.

Keywords

Right-angled triangle - A right-angled triangle has exactly one 90° interior angle.
Hypotenuse - A hypotenuse is the side of the right-angle triangle which is opposite the right-angle.
Pythagoras’ theorem - Pythagoras’ theorem shows that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of its longest side (the hypotenuse).