Answer:
The area is 243 square feet
Step-by-step explanation:
The perimeter of a rectangle is the sum of all four sides.
Two of the sides represent the length and two represent the width.
Given what we know and using l to represent the length and w to represent the width.
l + l + w + w = 72ft
or more concisely
2l + 2w = 72ft
The four sides all add together to equal 72ft
We also know that
l = 3w
This says the length is equal to 3 times the width
we have two unknowns, l and w, and now we have two related equations so we can solve for l and w.
The first thing we will do is replace l with 3w in the first equation because the second equation tells us that l is the same as 3w. Making the replacement gives us
2(3w) + 2w = 72ft
2 times 3w is 6w
6w + 2w = 72ft
6w plus 2w is 8w
8w = 72ft
Now if we divide both sides by 8 we maintain the equality since we are making the same change to both sides
8w / 8 = 72ft / 8
8w divided by 8 is 1w or just w and 72ft divided by 8 is 9ft
w = 9ft
So now we know the width is 9ft
if we now replace w with 9 in one of our original equations we can solve for l, let's use l = 3w
l = 3(9ft)
3 times 9 is 27 so
l = 27ft
So the length is 27ft which is 3 times the width of 9ft
The area of a rectangle is length times width or l x w, so
area = 27ft x 9ft
area = 243sqft
ft means feet and sqft means square feet
