Question

MEDAL FOR HELP NOT ANSWERS
The perimeter of a rectangle is 126 ft. The ratio of its length to its width is 5 : 4. What are the dimensions of the rectangle?

30 ft by 33 ft

35 ft by 28 ft

6 ft by 60 ft

3 ft by 60 ft

Answer 1

Well we know that a perimeter is the sum of all the sides

so for a rectangle we have

\[\large L + L + W + W = 126\]
or
\[\large 2L + 2W = 126\]

now given the ratio...we can say that for every 4 units of length for the width there are...there are 5 units of length for the length of the rectangle...so

\[\large 4L = 5W\]
or
\[\large L = \frac{5}{4}W\]

now if we plug that into our equation above we have

\[\large 2(\frac{5}{4}W) + 2W = 126\]
\[\large \frac{10}{4}W + 2W = 126\]
\[\large 10W + 8W = 504\]
\[\large 18W = 504\]
\[\large W = 28\]


and then just solve for L using the fact that W = 28