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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

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Answer

Given that the perimeter of the triangle is 72 cm, and the sides are in the ratio 3:4:5, we can represent the lengths of the sides as:

The sum of the sides (the perimeter) is:

$3x + 4x + 5x = 72$

This simplifies to:

$12x = 72$

To find the value of x, divide both sides by 12:

$x = \frac{72}{12} = 6$

Now, substituting x back into the expressions for the sides gives:

Step 2

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Answer

Using the formula for the area of a right-angled triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Here, we can take the two shorter sides (18 cm and 24 cm) as the base and height. Thus:

$\text{Area} = \frac{1}{2} \times 18 \times 24$

Calculating the area:

$\text{Area} = \frac{1}{2} \times 432 = 216 \text{ cm}^2$

So, the area of the triangle is 216 cm².

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