Question

the hypotenuse of a right triangle is 5 m more than twice shortest side and third side is 2 m less than the hypotenuse represent the situation as quadratic equation

Answer 1

Let, shortest side be X
Then, Hypotenuse = 2X+6
And, third side=2X+6-2
= 2X+4
Since, P^2+B^2=H^2
Therefore,
(2X+4)^2+X^2=(2X+6)^2
4X^2+16+16X+X^2=4X^2+36+ 24X
X^2-8X-20=0
X^2-10X+2X-20=0
X(X-10)+2(X-10)=0
(X+2)(X-10)=0
X=-2 or 10
Since, side can't be negative, therefore, X=10m=shortest side.
Hypotenuse = 2×10+6
=26m
Third side = 2×10+4
=24m

Answer 2

this is your answer