Question

The area of the isosceles triangle is 60 cm², and the length of each one of its equal side is 13cm. Find its base. 

Answer 1

Area of a isosceles triangle = `("b" xx sqrt (4"a"^2 - "b"^2))/4`

Here, area = 60, a = 13. Putting this in equation and squaring both sides, we get 

(60 x 4)² = b² (4 x 13 x 13 - b² )  

⇒  57600= b² x (676 - b²)  = 676 b² - b⁴ 

⇒ b⁴ - 676b² +57600 = 0 

⇒ b⁴ -100b² - 576b² + 57600 = 0 

⇒ b² (b² - 100) - 576 (b² - 100) = 0 

⇒ (b² - 100 )(b²  - 576) = 0 

⇒ b²  = 576 , b² = 100 

⇒ b = 24 , b = 10

⇒ Hence base can be either 24 or 10 cm.