Question

The hypotenuse of a right angled triangle is 6 m more than twice of the shortest side. The third side is 2 m less than the hypotenuse.

Answer 1

let the shortest side = x m
hypotenuse = 2x+6

third side = 2x+4

by Pythagorean theorem

square of hypotenuse = sum of other two squares

(2x+6)^2= x^2 +(2x+4)^2

(2x+6)^2-(2x+4)^2 =x^2

[(2x+6+2x+4)(2x+6-2x-4)] = x^2

we used a^2-b^2 = (a+b)(a-b)

(4x+10)2=x^2

8x+20= x^2

x^2-8x-20=0

x^2-10x+2x-20=0

x(x-10)+2(x-10)=0

(x-10)(x+2)=0

x-10=0 or x+2=0

x=10 or x= -2

x should not be negative

x=10m
third side = 2x+4= 2*10+4=24m

hypotenuse = 2x+6=2*10+6=26m

Answer 2

Step-by-step explanation:

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