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The perimeter of a right-angled triangle is 72 cm - Edexcel - GCSE Maths - Question 8 - 2018 - Paper 1

Question 8

The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5. Work out the area of the triangle.

Worked Solution & Example Answer:The perimeter of a right-angled triangle is 72 cm - Edexcel - GCSE Maths - Question 8 - 2018 - Paper 1

Step 1

Determine the lengths of the sides

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Answer

Let the sides of the triangle be represented as:

Base = 3x
Height = 4x
Hypotenuse = 5x

The perimeter of the triangle can be expressed as: $ext{Perimeter} = ext{Base} + ext{Height} + ext{Hypotenuse} = 3x + 4x + 5x = 12x$

Setting this equal to 72 cm gives: $12x = 72$

Solving for x yields: $x = 6$

Thus, the lengths of the sides are:

Base = $3 \times 6 = 18$ cm
Height = $4 \times 6 = 24$ cm
Hypotenuse = $5 \times 6 = 30$ cm

Step 2

Calculate the area of the triangle

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Answer

The area of a right-angled triangle is given by: $ext{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$ Substituting the base and height values: $ext{Area} = \frac{1}{2} \times 18 \times 24$ Calculating this gives: $ext{Area} = \frac{1}{2} \times 432 = 216 \text{ cm}^2$

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