A sand volleyball court has an area of 136 square meters and a perimeter of 50 meters. What are the dimensions of the volleyball court?

Question

I don't get how to do these problems.

Answer 1

Hello! This seems like it is a substitution problem! You will be using two equations. Remember that Area= length x width and perimeter (p) is equal to the sum of all sides. Here is the two equations. Let X equal one side and Y equal to another. 

 

A=xy 

P= 2x+2y

 

We substitute the given values 

136= xy 

50= 2x +2y 

 

We are going to solve for the second one since it’s a bit easier. We are going to solve for terms in X

 

2x+2y=50 

2x= -2y+50

x= -y+25

 

we plug in the values for X into the first equation from the start to solve for Y. 

 

136= (-y+25)y 

136= -y^2 +25y

 

this is now a polynomial, so set it equal to zero to factor. 

 

-y^2 +25y-136=0

 

-y^2 +17y+8y-136

 

(y-17)(y-8) 

 

so Y= 17, 8 

 

now use one of these values and plug it into equation where it will give me x instantly. 

 

x= -y+25

x= -(17) +25

x= 8 

 

Try it for the other Y: 

 

x=-8+25

x= 17 

 

So there you go, Answer is 

8meters X 17meters 

 

or 

 

17meters x 8meters

 

(both are the same answers)