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