A rectangular porch has dimensions of (x+1) feet and (x+3) feet. The area of the porch is 80 square feet. What are the length and width of the porch

Question

Lenght=x+3 width=x+1

Answer 1

Hi Bruce

 

The formula of the area of a rectangle is A = LW

You have been given the length and width as (x+1) and (x+3).  You've also been given the area, 80 ft²

 

So we can substitute what we have in the formula as follows

 

80 = (x+1)(x+3)

 

If we FOIL the right side of the equation, we have

 

80 = x²+4x+3

 

Let's bring the 80 to the right side of the equation so that we have an equation equal to 0.

 

x²+4x-77 = 0

 

We can factor this as

(x+11)(x-7) = 0

 

So, 

x+11 = 0  This gives us x=-11 which would yield dimensions of -10 and -8.  Since we can't have negative dimensions, let's check the other factor.

x-7=0, giving us x=7

So the dimensions of the porch are 

(7+1) and (7+3)

 

The porch is 8 x 10

Answer 2

Since length x width = area, you need to set up your equation as such:

 

(x+3)*(x+1) = 80

 

Distribute

x²+3x+1x+3 = 80

x²+4x+3 = 80

 

Set equal to 0

x²+4x-77 = 0

 

Factor:

(x-7)(x+11) = 0

x = 7 and x = -11.  Since lengths can't be negative, x =7.

 

But you're not done yet.  Plug 7 back into the original sides of x+1 and x+3.  You should get two numbers when multiplied together equaling 80.  Those two numbers will be your length and width.

 

Hope this helps!