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.
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:
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