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.

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.

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6 months 2021-08-04T06:49:25+00:00 1 Answers 8 views 0

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

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