Word problem. help!

Question

The shorter leg of a right triangle is 21 feet less than the other leg. Find the length of the two legs if the hypotenuse is 51 feet.

Answer 1

Draw a figure!

(x-21)² + x² = 51²

x²-42x+441+x² = 2601

2x²-42x-2160=0 => x² - 21x - 1080 =0

Quadratic formula yields an extraneous root and x = 45; the shorter side is 24.

Answer 2

Let x = the longer leg so the shorter leg is (x-21)

Now use the Pythagorean theorm x^2 + (x-21)^2 = 51^2

x^2 + x^2 -42x +441= 2601

2x^2 -42x -2160 =0 Divide both sides by 2 to make the math simpler

x^-21x-1080=0

(x-45)(x+24)=0

x=45. The other answer x= -24 should be discarded as you cannot have a negative length

So x=45 (longer leg)

x-21=24 (shorter leg)