SOLUTION: The perimeter of a rectangle is 30 inches. If its length is three times its width, find the dimensions

Question 954558: The perimeter of a rectangle is 30 inches. If its length is three times its width, find the dimensions
Found 2 solutions by macston, aYummyNoodle:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
W=width; L=length=3W; P=perimeter=2(L+W)=30 inches
P=2(L+W)
30 inches=2(L+W) Divide each side by 2.
15 inches=L+W Substitute for L.
15 inches=3W+W
15 inches=4W Divide each side by 4.
3.75 inches=W ANSWER 1: The width is 3.75 inches.
L=3W=3(3.75)=11.25 inches ANSWER 2: The length is 11.25 inches.
CHECK:
Perimeter=2(L+W)
30in=2(11.25in+3.75in)
30in=2(15in)
30in=30in
Answer by aYummyNoodle(10) (Show Source): You can put this solution on YOUR website!
We can assign the variable and to the length and width of the rectangle. In this case, I will assign to the length and to the width of the rectangle. As the length is three times its width, the equation would be:
.
Finding the perimeter of a rectangle is always the sum of two times the length and two times the width. stands for perimeter in this equation. That is:
.
In the first equation, we already have isolated, we can plug it in to the second equation. We know that the perimeter is 30, so we can also plug that in for .
.
Simplifying us would give us

.

So now we know that the width of the rectangle is 3.75.
We can now plug this back in to the original equation to get:

.
So the answer is Length=11.25 and Width=3.75.
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