Math I need help asap

Question

The length of a rectangle is 5 inches less than twice its width. It’s area is 88 inches squared. Find the length and width of the rectangle

Answer 1

The length of a rectangle is 5 inches less than twice its width. It’s area is 88 inches squared. Find the length and width of the rectangle

LENGTH - 5 = 2(WIDTH)

LENGTH • WIDTH = 88

LENGTH - 5 = 2(WIDTH)

LENGTH = 2(WIDTH) + 5

[2(WIDTH) + 5] • WIDTH = 88

W(2W+5)=88

2W² +5W = 88

2W² +5W - 88 = 0

FACTOR:

a = 2, b = 5, c = -88

c<0 (different signs)

b>0 (larger number is positive)

(w + ?)(w - ?)

ac= -176

what pairs of factors of -176 add up to 5? (try them all out)

factors: 1,176; 2,88; 4,44; 8,22; 11,16

(w + 16)(w - 11)= 0

w + 16 = 0 or w - 11 = 0

w= -16, 11

answer must be positive: w = 11

another way to find factors is to graph 2W² +5W - 88 = 0

where they cross the x-axis, are the 2 answers.

Thomas Hirschman