Question

The length of a rectangle is 7 ft less than three times the width, and the area of the rectangle is . Find the dimensions of the rectangle.

Answer 1

Answer:

See explanation

Step-by-step explanation:

the length of a rectangle is 7 feet less than three times it’s width. if the area of the rectangle is 180 ft, find the dimensions of the rectangle.

Width = x

Length = 3x - 7

Area of a rectangle = length × width

180 = (3x - 7) * x

180 = 3x² - 7x

3x² - 7x - 180 = 0

Using quadratic formula

a = 3

b = -7

c = -180

x = -b ± √b² - 4ac / 2a

x = -(-7) ± √(-7)² - 4(3)(-180) / 2(3)

x = 7 ± √49 - (-2160) / 6

= 7 ± √49 + 2160 / 6

x = 7 ± √2209/6

= 7 ± 47 / 6

= (7 + 47)/6 or ( 7 - 47)/6

= 54/6 or -40/6

x = 9 or -6.67

x cannot be negative

Therefore,

x = 9 ft

Width = x = 9 ft

Length = 3x - 7

=3(9) - 7

= 27 - 7

= 20 ft