the width of a rectangle is 1ft less than the length. the area is 30ft^2 .find the length and width

Question

Im trying to find the length and width of a rectangle.

Answer 1

Let L = the rectangle's length

Let W = its width

 

You have 2 unknowns (W and L) so you need two equations to solve for the unknowns.

 

Equation 1 - the width of a rectangle is 1ft less than the length

 

W = L - 1

 

Equation 2 -the area is 30ft^2

 

L*W = 30

 

Now substitute L-1 into equation 2 for W

 

L * (L-1) = 30     (Substitute L-1 for W)

 

L² - L -30 = 0     (Multiply out, subtract 30 from both sides)

 

(L-6)(L+5) = 0    (Factor the quadratic)

 

L = 6, -5

 

Can't have a negative length for a rectangle, so L = 6

 

W = L - 1