Question

The longer leg of a right triangle is 3m longer than the shorter leg. The hypotenuse is 6m longer then the side lengths of the triangle.Length of the shorter leg: _ cmLength of the longer leg:__ cmLength of hypotenuse __ cm

Answer 1

Let the length of the shorter leg is x.

The length of the the longer leg will be (x+3) m.

The length of the hypotenuse will be (x+6) m.

Applying the pythagorus theorem,

`\begin{gathered} (x+6)^2=x^2+(x+3)^2 \\ x^2+36+12x=x^2+x^2+9+6x \\ x^2-6x-27=0 \\ x^2-9x+3x-27=0 \\ x(x-9)+3(x-9)=0 \\ (x-9)(x+3)=0 \\ x=9\text{ \& -3} \end{gathered}`

Neglecting the negative value of x.

Length of the shorter leg: 9 cm

Length of the longer leg: 9+3 cm=12 cm

Length of hypotenuse: 9+6 cm= 15 cm.