Question

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

Answer 1

Answer:

Step-by-step 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