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Question
The perimeter of the right angled triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle.
Solution
Perimeter = a+b+h where a and bare sides and his hypotenuse. Here h= 25.
Given that a+b+ 25=60, hence a+b=35
⇒ a=35 - b ... (i)
Also, a2 + b2 = h2 = 625 ... (ii)
Putting (i) in (ii), we get,
(35 - b)2 + b2 = 625,
1225 + b2 -70 b + b2 = 625
2b2 - 7O b + 600 = 0 ,
Dividing by 2, we get: b2 - 35b + 300 = 0
⇒ b2 - 20b - 15b + 300 = 0
⇒ b(b-20)-15(b-20)=0
⇒ (b-20)(b-15)=0
⇒ b= 20 or 15
Hence if b = 20, a = 35 - 20 = 15 and area = `(20 xx 15)/2 = 150` cm2
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