Question

The perimeter of a rectangle is 162 ft. The ratio of the length to the width is 5:4. Find the length of the rectangle.

Answer 1

45ft.

Answer 2

first find the constant 2(5x+4x)=162
then *5

Answer 3

2L + 2W = 162

4L = 5W

L = \(\large \frac{5}{4}W\)
Substitute that into the 1st equation we have

\[\large 2(\frac{5}{4}W) + 2W = 162\]
\[\large \frac{10}{4}W + 2W = 162\]
\[\large \frac{10 + 8}{4}W = 162\]
\[\large 18W = 648\]
\[\large W = 36\]

If W = 36...then

2L + 2(36) = 162
2L + 72 = 162
2L = 90
L = 45

Now...is

\[\large \frac{45}{36} = \large \frac{5}{4}\]
Looks like both 45 and 36 are divisible by 9 so...45/9 = 5 and 36/9 = 4 so yes it is correct

Length = 45