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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
Calculate the lengths of the sides
Answer
Given the sides are in the ratio 3:4:5, let the common multiple be (x). Thus:
- Side 1 = (3x)
- Side 2 = (4x)
- Side 3 = (5x)
The perimeter is given by:
[ 3x + 4x + 5x = 72 ]
Combining like terms gives:
[ 12x = 72 ]
Now, solving for (x):
[ x = \frac{72}{12} = 6 ]
Now, substituting back, we find the actual lengths:
- Side 1 = (3 \times 6 = 18) cm
- Side 2 = (4 \times 6 = 24) cm
- Side 3 = (5 \times 6 = 30) cm
Step 2
Calculate the area of the triangle
Answer
Since this is a right-angled triangle, the area can be calculated using the formula:
[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ]
We can take Side 1 (18 cm) as the base and Side 2 (24 cm) as the height. Thus:
[ \text{Area} = \frac{1}{2} \times 18 \times 24 ]
Calculating gives:
[ \text{Area} = \frac{1}{2} \times 432 = 216 ]
Therefore, the area of the triangle is (216 , \text{cm}^2).