Question

The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.

Answer 1

Let hypotenuse=h, and other sides by x and y (x bigger than y). As per the question, 

h= 2y + 1, x = y + 7 .... (i) 

For right angled triangle, x² + y² = h² ... (ii) 

Putitng (i) in (ii), we get: 

(y+ 7)² + y² = (2y+1)² 

⇒ y² + 49 + 14y + y² = 4y² +1 + 4y 

⇒ 2y² -10 y - 48 = 0 

⇒ y² - 5y - 24 = 0 

⇒ y² - 8y + 3y - 24 = 0 

⇒ y (y - 8) + 3 (y - 8) = 0 

⇒ (y+3) (y-8) = 0 

⇒ y = 8 

⇒ x=y+ 7= 15, h = 2 x 8+ 1 = 17 

Hence the sides are 8, 15, 17 cm.