Question

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

Chap : Quadratic Equations , Class 10 .

Plz help !!

Answer 1

let the length of the shortest side be x
so the length of the hypotenuse is 2x+1
and the length of the third side =x+7
on applying phythagoras theorem we get
x²+(x+7)²= (2x+1)²
x²+x²+14x+49=4x²+4x+1
10x+48=2x²
x²-5x-24=0
x²-8x+3x-24=0
x(x+3)-8(x+3)=0
(x-8)(x+3)=0
x=8
so the sides are 8,15,17

Answer 2

Hello friend!
Here's ur answer!
Let the length of the shortest side be x
Length of the hypotenuse is = 2x+1 Length of the third side = x+7

x2 +(x+7)2= (2x+1)2
x2+x2+14x+49=4x2+4x+1
10x+48=2x2
x2-5x-24=0
x3-8x+3x-24=0
x(x+3)-8(x+3)=0
(x-8)(x+3)=0
x=8 or x =- 3
As x cannot be negative,
X = 8
The sides are 8,15,17.