Question

The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle.

Answer 1

Let ABC be a right-angled triangle.

Since the perimeter of the right triangle is 60 cm, 

AB + BC +CA = 60 cm

⇒ AB + BC + 25 = 60

⇒ AB + BC = 35 cm          .....(1)

In ∆ABC,

AB² + BC² = CA²

⇒ (AB + BC)² − 2(AB)(BC) = (25)²

⇒ (35)² − 2(AB)(BC) = (25)²                                     [From (1)]

⇒ (35 − 25)(35 + 25) = 2(AB)(BC)'

⇒ (AB)(BC) = 300

Now,

Area of ∆ABC= `1/2`×AB×BC=`1/2`×300=150 cm²

Hence, the area of the triangle is 150 cm².