a rectangle has a length of 6x-5 feet and a width of 2x+9 feet. Find the perimeter

Question

a rectangle has a length of 6x-5 feet and a width of 2x-9 feet.  Find the perimeter of the retangle.

 

 

Answer 1

Hi Kerry;

length, 6x-5 feet

width, 2x+9 feet.

Your first priority would be to make certain your units match.  The length and width are provided in feet.  But sometimes, you may find one unit in yards or inches.

 

We know that a rectangle has four sides, two of length and two of width.

perimeter=2(6x-5)+2(2x+9)

Let's distribute the 2...

perimeter=12x-10+4x+18

Let's combine like terms...

perimeter=16x-8

or

perimeter=8(2x-1)

 

Answer 2

Hi Kerry,

 

I'm assuming that there were no values given for x, so this is just a "combining like terms" problem.

 

I would first rewrite 6x -5 as 6x + (-5) so that we can use the commutative property of addition and rearrange everything.

 

I'd draw a rectangle on my paper, labeling the information that I know, which is the length and the width. Since it's a rectangle, we know that the other length and width are still the same as the values that are given, so our 2 lengths and 2 widths are:

 

6x + (-5)

6x + (-5)

2x + 9

2x + 9

 

You can then take the sum of those 4 terms by rearranging in whatever order suits you best. Remember that 6x + 6x would give us 12x (hopefully your teacher has already covered combining like terms if you've been assigned this!)

 

Hope this helps!