The perimeter of a right-angled triangle is 60 cm. The lengths of its sides are in the ratio 3 : 4 : 5. Calculate the area of the triangle.
We are given ratios of side lengths and the total perimeter. The perimeter of the triangle is simply the sum of the side lengths. Imagine that the sides are made up of "units": 3 times a unit + 4 times the same unit + 5 times the same unit is equal to the perimeter (based on the ratios). Mathematically: 3x+4x+5x = 60, x = 5cm. So one of these "units" is equal to 5cm, which means the sides are 35=15 cm, 45 = 20 cm and 55 = 25 cm (Double check: 15+20+25 = 60 indeed!) Because the triangle is right-angled, the longest side is the hypotenuse and the two shorter sides are the legs. The area of a right-angled triangle can be calculated by multiplying the length of the two legs and dividing it by 2: 1520/2 = 150cm2
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