Question

A rectangle's width is 5 feet less than its length. If the area of the rectangle is 546 square feet, what is its length, in feet?

Answer 1

W = width
L = length

First sentence says: W = L - 5

Second sentence says: L * W = 546


plug first into second and solve. so L*(L - 5) = 546

let me know if i should continue ^_^

Answer 2

Sorry my connection just went off, so the length would be 13 right ?

Answer 3

nope. from the last line we have

\[L^2 - 5L -546 = 0\]

you can solve this using the quadratic equation or completing the square.

using quadratic:\[\frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a }\]
\[\frac{ 5 \pm \sqrt{25 - (4*1*-546)} }{ 2*1 } = \frac{ 5 \pm \sqrt{2209} }{ 2 } = \frac{ 5 \pm 47 }{ 2 }\]

one of these two answers (using minus on the plus/minus sign) ends up negative, so we can ignore it. negative length doesn't make sene.

answer is 26