Question

11. The perimeter of rectangle DOGS is 408 cm. The ratio of the length to width is 5:7. What is thewidth of the rectangle?

Answer 1

The width of the rectangle DOGS is 119cm

To solve this, since is a ratio problem, we know that the two ratios must add to the total. This is, for a ratio of 5:7, 5 + 7 = 12 is the total "divisions" for the ratio.

This means that if 12 of 12 parts add to the perimeter (408cm):

$\frac{5}{12}+\frac{7}{12}=\frac{12}{12}$

12/12 represents the perimeter 408cm.

The, we can divide the perimeter by 12 and get:

$\frac{408}{12}=34$

Since the width is 7/12 of the perimeter:

$34\cdot7=238$

But, we are taking the perimeter of a rectangle, which is twice the width plus twice the length, thus we need to divide this number by 2:

$\frac{238}{2}=119$

And we get the final answer of 119cm