the area of a rectangle is 21ft^2 , and the length of the rectangle is 1 ft less than twice the width. find the dimensions of the rectangle.

Question

i am doing summer school, and  i can not remember the format/equations to use while solving the dimensions of a rectangle. some help would be great!

Answer 1

l = 2w - 1

 

A = l * w

 

Substitute l into area equation:

 

A = (2w - 1) * w

 

A= 2w^2 -w = 21

 

2w^2 - w -21 = 0.  Solve for w using quadratic formula.  a = 2, b = -1 and c = -21

 

[-b±√(b² - 4ac)]/2a

 

[1± √((-1)^2 - 4*2*(-21))]/(2*2)

 

[1± √(1+168)]/4

 

w = 3.5 ft

 

l = 2w - 1 = 2*3.5 - 1 = 6 ft

 

Check: A = l*w = 3.5 * 6 = 21 ft²

 

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