21) ratio of length question

Question

21) 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? 

Answer 1

Since x>y , y is the shortest side.

 

Perimeter = 8y

 

2(x + y) = 8y

 

 

Divide both sides of the equation by 2.

 

x + y = 4y

 

 

Subtract y to both sides of the equation to solve for x.

 

x = 3y

 

We use this fact to find ratio of y to x.  That is y/x.

 

Divide both sides of the equation by x.

 

1 = 3y / x

 

 

Multiply both sides of the equation by 1/3.

 

1/3 = y / x