Question

The length of the longer leg of a right triangle is 6cm more than twice the length of the shorter leg. The length of the hypotenuse is 9cm more than twice the length of the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg:
cm
Length of the longer leg:
cm
Length of the hypotenuse:
cm

Answer 1

Same as the one before a few way back.... so...check the picture below, then we use the pythagorean theorem

$\bf (2s+9)^2=s^2+(2s+6)^2 \\\\\\ 4s^2+36s+81=s^2+4s^2+24s+36\implies 36s+81=s^2+24s+36 \\\\\\ 0=s^2-12s-45\implies 0=(s-15)(s+3)\implies \begin{cases} 0=s-15\\ \boxed{15=s}\\ -----\\ 0=s+3\\ -3=s \end{cases}$