Question

The perimeter of a right triangle is 60 CM. Its hypotenuse is 25 cm. find the area of the triangle?

Answer 1

let the given right angled triangle be ΔABC right angled at B

hypotenuse = AC = 25 cm

perimeter = 60 cm

AB²+BC²=AC² (by Pythagoras theorem)

AB²+BC²=625

(AB+BC)²-2*AB*BC=625

since AB+BC+AC=60

AB+BC+25=60 or AB+BC=35

35²-2AB*BC=625

2*AB*BC=1225-625=600

dividing by 4 on both sides, we get

½AB*BC=150

i.e area(ΔABC) = 150cm²

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