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

Answer:

Lenght: $53\ feet$

Width: $28\ feet$

Step-by-step 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":

$2l+2(28)=162\\\\2l=162-56\\\\l=\frac{106}{2}\\\\l=53$