The length of a rectangle is three more than twice the width, and the perimeter is 36 inches. What is the rectangles area?

Question

I've been stuck on this for a while now, please helppp!!!

Answer 1

Hi Lucia,

 

This is a problem where you have to set up two equations, then solve them using elimination or substitution.

 

Let L = length and W = width.

 

1) "The length of a rectangle is three more than twice the width." This can be written in a math sentence as

 

L = 2W + 3

 

where "twice the width" is 2W and "three more" is just adding 3.

 

2) "Perimeter is 36 inches". Recall the formula for the perimeter of a rectangle

 

P = 2W + 2L

 

we set the formula to 36 and that gives us our second equation: 36 = 2W + L

 

You would then use either substitution or elimination techniques to solve for the actual values of W and L. I'll give you a chance to do that on your own!

 

 

Answer 2

For this question, you need to figure out the length and the width because the area is directly related to them (A = l*w).

 

What we do know is that the perimeter is 36 inches. Since the perimeter is equal to P = 2l + 2w, we can say:

P = 36 = 2(3 + 2w) + 2(w), where the length l is 3 + 2w

 

Solve for w first, then solve for l. Use these values to find the area.