a rectangular table has an area of 27 square feet and a perimeter of 24 feet. what are the dimensions of the table?

Question

a rectangular table has an area of 27 square feet and a perimeter of 24 feet. what are the dimensions of the table?

Answer 1

Hello Jansen,

 

So we know the formula for area is:

A=LW

And perimeter is:

P=2L+2W

 

We know area is 27 and perimeter is 24, so our equations are:27=LW

24=2L+2W

 

To solve as a system of equations, lets isolate L on the second equation.

24 = 2L + 2W

24 -2W = 2L

12 - W = L

 

And Plug this into the first equation

27 = (12-W)W

27 = 12W - W²

 

This looks like a quadratic, so let's bring everything to the left side and factor.

W² - 12W + 27 = 0

(W-9)(W-3)=0

W=9 or W=3

 

Plug both of these into 27=LW to find L

27=9L

L=3 when W=9

or 27=3L

L=9 when W=3

 

These both say pretty much the same thing, so this table is 9 feet long and 3 feet wide.