MATH SOLVE

2 months ago

Q:
# 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?

Accepted Solution

A:

Answer: Lenght: [tex]53\ feet[/tex] Width: [tex]28\ feet[/tex]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: [tex]P=2l+2w[/tex] Where "l" is the lenght and "w" is the width. Set up a system of equations: [tex]\left \{ {{2l+2w=162} \atop {8l+5w=564}} \right.[/tex] Using the Elimination Method, multiply the first equation by -4, add the equations and then solve for "w": [tex]\left \{ {{-8l+-8w=-648} \atop {8l+5w=564}} \right.\\..........................\\-3w=-84\\\\w=28[/tex] Substitute the value of "w" into any original equation of the system and solve for "l": [tex]2l+2(28)=162\\\\2l=162-56\\\\l=\frac{106}{2}\\\\l=53[/tex]