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# A rectangle’s length is 99 feet shorter than three times its width.

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A rectangle’s length is 99 feet shorter than three times its width.

The rectangle’s perimeter is 222 feet.

Find the rectangle’s length and width.

Mar 24, 2021

#1
+2

We know that Perimeter is the sum of all the sides lengths.
Let's call perimeter, p.
Base length, b.
Height length, h.
P = b + h + b + h
P = 2b + 2h
P = 2(b+h)

The problem said that the length/base is 99 feet shorter than 3 times the width.
So the corresponding equation would be...
b = 3w - 99

Now we can substitute b for our equation into the original equation.
P = 2[(3w-99) + w]

According to the problem, the perimeter is 222.
So we can substitute 222 for P.
222 = 2[(3w-99) + w]

Now the last thing we have to do is solve!
222 = 2[(3w-99) + w]
111 = (3w-99) + w
111 = 3w - 99 + w
111 = 4w - 99
210 = 4w
w = 52.5

To find the length, we just substitute the value of w into the equation b = 3w - 99, which is listed above.
b = 3(52.5) - 99
b = 157.5 - 99
b = 58.5

Width = 52.5
Length or Base = 58.5

Mar 24, 2021

#1
+2

We know that Perimeter is the sum of all the sides lengths.
Let's call perimeter, p.
Base length, b.
Height length, h.
P = b + h + b + h
P = 2b + 2h
P = 2(b+h)

The problem said that the length/base is 99 feet shorter than 3 times the width.
So the corresponding equation would be...
b = 3w - 99

Now we can substitute b for our equation into the original equation.
P = 2[(3w-99) + w]

According to the problem, the perimeter is 222.
So we can substitute 222 for P.
222 = 2[(3w-99) + w]

Now the last thing we have to do is solve!
222 = 2[(3w-99) + w]
111 = (3w-99) + w
111 = 3w - 99 + w
111 = 4w - 99
210 = 4w
w = 52.5

To find the length, we just substitute the value of w into the equation b = 3w - 99, which is listed above.
b = 3(52.5) - 99
b = 157.5 - 99
b = 58.5

Width = 52.5
Length or Base = 58.5

Guest Mar 24, 2021