Question 90350
Find the length of the legs of a right triangle if the area is 250 sq.in. and one leg is 5" more than the other leg.
Starting with the formula for the area of a triangle: {{{A = bh/2}}}
A = 250 sq.in.
let b = x, then h = x+5, so...
{{{250 = x(x+5)/2}}} Multiply both sides by 2.
{{{500 = x(x+5)}}} Perform the indicated multiplication on the right side.
{{{500 = x^2+5x}}} Put this into the standard form for quadratic equations ({{{ax^2+bx+c = 0}}}) by subtracting 500 from both sides.
{{{x^2+5x-500 = 0}}} Factor this trinomial.
{{{(x+25)(x-20) = 0}}} Apply the zero products principle.
{{{x+25 = 0}}} or {{{x-20 = 0}}}
{{{x = -25}}} or {{{x = 20}}} Discard the negative solution as side lengths are positive.
{{{x = 20}}}inches, and...
{{{x+5 = 25}}}inches.
The legs are: 20 inches and 25 inches.

Check:
{{{A = (20)(25)/2}}}
{{{A = 500/2}}}
{{{A = 250}}}sq.in.