The semi-perimeter of a triangle is 72cm and its sides are in the ratio 3 : 4 : 5. Find the area of the triangle.
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Step-by-step explanation:
Begin by working out the length of the three sides.
Because the sides are in a ratio of 3:4:5 and the perimeter is 72
3x + 4x + 5x = 72 : combine like terms
12x = 72 : isolate x by dividing both sides by 12
x =6
The sides are 18 cm, 24 cm and 30 cm.
In a right triangle the two shorter sides are always perpendicular, so the area of any right triangle is: A = (1/2) • s₁ • s₂ where s₁ and s₂ are the two shorter sides.
A = (1/2) • 18 cm • 24 cm = 216 cm²
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