the length of a rectangle is 10 more than its width. the area is 336 square feet. find the length and width of the rectangle

Answer 1

L = w+10. And area = w (l). Rewrite area as. w (w+10) = 336.

Dist. Prop. Gives w² + 10w = 336

Subtract 336 from each side gives

w² +10w -336 = 0. Time to see what factors we can use to get 336 that are 10 apart.

336 = 3 x 112. Factors 3 and 112 are not 10 apart. Take a 2 factor from 112 and give it to the 3, producing 6 x 56 but factors are not 10 apart. Repeat with the 56, taking out a factor of 2 and giving it to 6, making 12 x 28.

Factors are getting closer, differing by 16 (28-12). Repeat take factor of 2 from 28, leaving 24 x 14. These are 10 apart. So,

w2 +10w - 336 =0 factors into

(w + 24)(w -14) = 0. Notice that +24 and -14 will add up to the positive 10.

So, either (w + 24) = 0 or (w - 14) = 0

Solve for w. w = -24 or w=14. Width can't be negative, so discard the -24. We are left with w=14. Length = w + 10 = 14 + 10 = 24. Length is 24 inches , width is 14 inches.

alternative method, apply quadratic formula to w² + 10w - 336 = 0. Remember to throw out the negative value of w = -24.