Nathan B. answered • 07/16/18

Tutor

5
(20)
Elementary and Algebraic skilled

Here's what we know:

A = Lw (rectangular area is equal to length times width)

A = 1675.6

L = w + 2.3 (the height (length for purposes of the equation) is 2.3 feet more than width)

Plug in the variable-values:

1675.6 = w(w + 2.3)

1675.6 = w

^{2}+ 2.3w0 = w

^{2}+ 2.3w - 1675.6Quadratic formula:

x = (-b ± √(b

^{2}- 4ac)) / 2aw = (-2.3 ± √(2.3

^{2}- 4 * 1 * -1675.6)) / (2 * 1)Simplify

w = (-2.3 ± √(5.29 + 6702.4)) / 2

w = (-2.3 ± √6707.69) / 2

w = (-2.3 ± 81.9) / 2 (this is where that rounding need came into play)

w = (-2.3 + 81.9) / 2 ; x = (-2.3 - 81.9) / 2

We can't have a negative length/width, so we can throw out the second possibility:

w =

^{-2.3 + 81.9}/_{2 }w =

^{79.6}/_{2}w = 39.8

Find L:

L = 39.8 + 2.3

L = 42.1

Check:

42.1 * 39.8 ≈ 1675.6

1675.58 ≈ 1675.6