Question

K

The perimeter of a rectangular sports court is 148 feet. After a game, a player's coach estimates that the athlete has run
a total of 353 feet, which is equivalent to four times the court's length plus seven times its width. What are the
dimensions of the sports court?
The length is
feet.

Answer 1

Answer: Let's call the length of the rectangular court "L" and the width "W". Then, the perimeter of the court is 2 * (L + W) = 148 feet, so 2 * L + 2 * W = 148 feet.

And, according to the coach's estimate, the athlete ran a total of 4 * L + 7 * W = 353 feet.

We can use these two equations to find the dimensions of the court. Solving the first equation for W:

W = (148 - 2 * L) / 2.

Substituting this expression for W into the second equation:

4 * L + 7 * (148 - 2 * L) / 2 = 353

Expanding and simplifying the right side of the equation:

4 * L + 74 - 7 * L = 353

-3 * L = -279

L = 93 feet.

Finally, using the expression for W from the first equation:

W = (148 - 2 * L) / 2 = (148 - 2 * 93) / 2 = 32 feet.

So the dimensions of the sports court are 93 feet by 32 feet.

Explanation: