The length of one leg of a right triangle is 8ft. The length of the hypotenuse is 4 feet longer than the other leg. Find the length of the hypotenuse and the other leg.

Question

deoxna · Answer

Let x be the length of the other leg. So, because of the Pythagorean theorem: $$x ^{2}+8^{2}=(x+4)^{2}$$
$$x ^{2}+64=x ^{2}+8x+16$$
Cancel out the x^2, so: 64=8x+16; 48=8x; x=6
The length of the shorter leg is 6ft
The hypotenuse is 4 more than that so 6+4= 10ft