+409 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.
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
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
