AC9M8M06Year 8MeasurementPractised on site

AC9M8M06 — Year 8 Measurement

Official Curriculum Content Description:

use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles

Worked Examples (1)

Example 1Pythagoras' Theorem in Right-Angled Triangles

A right-angled triangle has shorter sides of length

10\text{ cm}

and

22\text{ cm}

. Calculate the length of the hypotenuse

x

. Give your answer to 1 decimal place.

Diagram not accurately drawn

Common mistake: Adding the side lengths directly (

a + b

) without applying Pythagoras' theorem (

a^2 + b^2 = c^2

Correct Answer:

24.2\text{ cm}

Accepted: A unit is optional (cm accepted).

Worked Solution:

1. Use Pythagoras' theorem:

c^2 = a^2 + b^2

. 2.

x^2 = 10^2 + 22^2 = 100 + 484 = 584

. 3.

x = \sqrt{584} \approx 24.2

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