The perimeter of a rectangle with adjacent side lengths of x and y, where x>y, is 8 times as great as the shorter side of the rectangle. What is the ratio of y to x?

A. 1:2
B. 1:3
C. 1:4
D. 2:3
E. 3:4

since p = 2(x+y) = 8y,

x+y = 4x
x = 3y

y:x = 1:3

Thanks steve! Very helpful

Let's use the given information to set up an equation.

The perimeter of a rectangle is given by the formula: Perimeter = 2(x + y), where x and y are the side lengths of the rectangle.

According to the problem, the perimeter of the rectangle is 8 times as great as the shorter side. So, we can write the equation as: 2(x + y) = 8y.

Now, let's solve this equation step-by-step to find the ratio of y to x.

1. Distribute the 2 on the left side: 2x + 2y = 8y.
2. Subtract 2y from both sides to isolate the variable x: 2x = 6y.
3. Divide both sides by 2 to solve for x: x = 3y.

Now we know that the longer side of the rectangle (x) is 3 times the length of the shorter side (y).

Therefore, the ratio of y to x is 1:3, which is answer choice B.

To solve this problem, we can start by using the information given.

Let's assume that the shorter side of the rectangle is y. The longer side is x.

We can write the equation for the perimeter of the rectangle as:

Perimeter = 2x + 2y

According to the problem, the perimeter of the rectangle is 8 times as great as the shorter side. So we can write this as an equation:

2x + 2y = 8y

Now let's simplify this equation:

2x = 8y - 2y
2x = 6y
x = 3y

Now we have a relationship between x and y. The ratio of y to x can be written as:

y : x = 1 : 3

So the ratio of y to x is 1 : 3.

Therefore, the correct answer is D. 2:3.