Question

The perimeter of a rectangular sports court is 162 feet. After a game, a players coach that the athlete has run a total of 564 feet which is equivalent to eight times the court length plus five times it’s width what are the dimensions of the sports court?

Answer 1

Lenght:
`53\ feet`

Width:
`28\ feet`

Explanation:

The complete exercise is: "The perimeter of a rectangular sports court is 162 feet. After a game, a players coach estimates that the athlete has run a total of 564 feet which is equivalent to eight times the court length plus five times it’s width what are the dimensions of the sports court?"

The perimeter of a rectangle can be calculated with:

`P=2l+2w`

Where "l" is the lenght and "w" is the width.

Set up a system of equations:

`\left \{ {{2l+2w=162} \atop {8l+5w=564}} \right.`

Using the Elimination Method, multiply the first equation by -4, add the equations and then solve for "w":

`\left \{ {{-8l+-8w=-648} \atop {8l+5w=564}} \right.\\..........................\\-3w=-84\\\\w=28`

Substitute the value of "w" into any original equation of the system and solve for "l":

`2l+2(28)=162\\\\2l=162-56\\\\l=(106)/(2)\\\\l=53`