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 to the rectangle. what is the ratio of y to x?
a. 1:2
b. 1:3
c. 1:4
d. 2:3
is b the answer?
yes
To find the ratio of y to x, we first need to set up equations based on the given information.
Let's assume that the shorter side of the rectangle is y. According to the problem statement, the perimeter of the rectangle is 8 times as great as the shorter side.
The perimeter of a rectangle is given by the formula: 2 * (length + width).
In this case, the length is x and the width is y. So, the equation becomes: 2 * (x + y) = 8y.
Simplifying the equation, we get: 2x + 2y = 8y.
Now, let's solve for x in terms of y:
2x = 8y - 2y
2x = 6y
x = 3y
So, the ratio of y to x is y:x, or 1:3.
Therefore, the correct answer is d. 2:3.