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,

AB^{2} + BC^{2} = CA^{2}

⇒ (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 cm^{2}

Hence, the area of the triangle is 150 cm^{2}.

Concept: Area of a Triangle

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