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

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

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Solution

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.

Concept: Area of a Triangle
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