Question

The length of the sides forming a right angle in a triangle are 5x cm and (3x-1) cm. If the area of the triangle is 60cm², find the hypotenuse.

Answer 1

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

Here, Height and base are 5x and (3x-1) and the area is 60 

Hence , `5x xx (3x - 1) xx 1/2 = 60`

⇒ 15x² - 5x = 120 

⇒ 3x² - x -24 = 0 

⇒ 3x² - 9x + 8x - 24 = 0 

⇒3x (x - 3) +8(x - 3) = 0 

⇒ (3x + 8)(x - 3) = 0,  hence x = 3.

Sides are 5 x 3 and 3 x 3-1= 15 and 8 ems. 

⇒ Hence, h²= 15² + 8² = 289 

Hypotenuse = 17 cms.