Word question see below

Question

A rectangle sign must have an area of 18 yd.². It’s length must be 4 yards more than it’s width. Find the dimensions of the sign.

Answer 1

Length x width = area

Let w be equal to x

Let L be equal to x + 4

x (x+4) = 18

x² + 4x = 18

x² + 4x - 18= 0

Figure it out through FOIL, first, outside, inside, last

Find multiples of -18 that will add up to 4

In order to get to -18, one factor needs to be positive, and one needs to be negative.

Possible factors of -18: -9 and 2, -2 and 9, -6 and 3, -3 and 6, -1 and 18, -18 and 1.

Since adding these factors will not add up to 4, we must use the quadratic equation.

a= 1

b= 4

c= -18

-4 +/- √ (4² - 4 (1) (-18) ) all divided by 2 (1)

-4 +/- √16 + 72 all divided by 2

-4 +/- √88 all divided by 2

-4 +/- 9.38 all divided by 2

Normally, there are two possibilities, but the only one that gives a positive number is (-4 + 9.38) divided by 2

5.38 divided by 2= 2.69

Width = 2.69 yds

Length= 6.69 yds