Question

A rectangle has a length that is 9 inches less than twice its width. The area of the rectangle is 180 square inches.

a. Write an equation that represents the situation.
b. Find the length and width of the rectangle.
c. Find the perimeter of the rectangle.
pls help lols

Answer 1

Explanation:

a) Let the width = w

Two times its width = 2*w = 2w

9 inches less than 2w = 2w - 9

Length = 2w - 9

Area of rectangle = length *width = 180 square inches

(2w - 9 ) * w = 180

2w*w - 9*w = 180

2w² - 9w - 180 = 0

b) sum = -9

Product= -360

Factors = -24 , 15 {15 *[-24] = -360 and 15 + (-24) = -9 }

2w² - 9w - 180 = 0

2w² - 24w + 15w - 180 = 0

2w(w - 12w) + 15(w - 12) = 0

(w -12) (2w + 15) = 0

{Ignore 2w + 15 = 0 as measurements cannot be a -ve value}

w - 12 = 0

w = 12 inches

l = 2w -9

= 2*12 - 9

= 24 - 9

l = 15

length = 15 inches

Width = 12 inches

c) Perimeter = 2 *(length + width)

= 2*(15 + 12)

= 2 * 27

= 54 inches