Precalc? Determining the area of a rectangle given its perimeter? PLEASE HELP!!?

Question

The length of a rectangular garden is 8 feet longer than its width. If the garden's perimeter is 188 feet, what is the area of the garden in square feet?

 

 

 

I am really stuck on this and I am not sure what the process is for solving this. Thank you for your time and help in advance! I really appreciate it!

Answer 1

The area of a rectangle is length*width.

We need to determine the length and width of the

rectangle and then multiply those values to find

the area.

 

Since the length is 8ft more than the length then

if the width is w, then the length is w+8

 

The perimeter is the distance around the outside of

the figure, so in this case it is:

 

2L + 2W

but l = w+8 so we have

 

2(w+8) + 2w = 188

distribute the 2 through the parenthesis

2w + 2(8) + 2w = 188

2w + 16 + 2w = 188

combine like terms

4w + 16 = 188

subtract 16 from both sides

4w = 172

divide both sides by 4

w = 172/4

w = 43 ft

 

l = w+8 = 51 ft

 

We no have the length and width.  Area = l*w

 

A = 43(51) = 2193 ft²

Answer 2

there are a few ways to solve this...your teacher taught you at least one way: lets solve this using one variable unknown...

 

always write out what you know...

 

rectangle...hmm?  that means 4 sides with opposite sides being equal...whew! that is a lot of good information...

 

lets form an equation in words:

 

if width is lets say the unknown X, then the unknown length must be (X+8)...for it says it is 8 feet longer...right?

 

so... 2 opposite sides must be X while the other 2 opposite sides must be (X+8)...so lets form our equation...the total perimeter of a rectangle = the sume of all the 4 sides or...

 

X   +   X  +    (X+8)    +    (X+8)  =   188

 

combine and reduce..... 4X + 16   =   188

 

simplify.......                  4X = 172

and.............                    X = 43      so 2 sides are 43 feet while the other 2 sides are 43+8 or 51 feet

 

sanity check......  43 +  43   +   51    +   51 = what....thats right, 188   How about that?...good luck!