Question

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

Answer 1

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