Question

The area of right-angled triangle is 600cm². If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.

Answer 1

Area of a triangle = `("Height"  xx  "Base")/2`

Here, Height and base are x and (x + 10 ) and the area is 600 

Hence , `x xx (x + 10) xx 1/2 = 600`

⇒ x² + 10x= 1200 

⇒ x² + 10 x - 1200 = 0 

⇒ x² + 40x - 30 x - 1200 = 0 

⇒ x (x + 40} - 30(x + 40) = 0 

⇒ (x + 40)(x - 30) = 0, hence x = 30 .

Base = 30+ 10 = 40 cms.

Hence h²= 40² + 30² = 2500