The area of a right triangle is 16 square miles. One leg of the triangle is 4 miles longer than the other leg. Find the length of each leg.

Answer:8 miles and 4 milesStep-by-step explanation:Area of a triangle = 1/2 bh = 16 square milesFrom the question, one of the legs is 4 miles greater than the other legLet's pick b; the breadth as the longer leg and h; the height as the shorter legSo, b = 4 + hNow, we'll slot in the values of b and h This gives; 1/2 ( 4 + h ) * h = 16Cross multiply ( 4+ h ) * h = 2(16)4h + h^2 = 32Let's equate the equation to zero to form a quadratic equation4h + h^2 - 32 = 0Rearrangeh^2 + 4h - 32 = 0Two numbers that when they are multiplied give - 32 and when they are summed up give +4 are +8 and -4Slot in these numbers in the equationh^2 + 8h - 4h - 32 = 0h( h + 8 ) -4 ( h + 8 ) = 0( h + 8 ) ( h - 4 ) = 0h + 8 = 0                       h - 4 = 0h = -8                            h = 4Taking the positive value of h, we have that h = 4 milesNow let's substitute the value of h in b = 4 + hb = 4 + 4b = 8 milesCheck16 = 1/2 *8*416 = 1/2 * 3216 = 16Therefore, the length of the longer side is 8 miles and that of the shorter side is 4 miles