Question

the length of a new playing field is 7 yards longer than quadruple the width. if the perimeter of the rectangle playing field is 494 yards, what are the dimensions?

Answer 1

So you're looking at the following:

--------------------------
- -
W - -
- -
--------------------------
L

Where L is the length of the rectangle and W is the width, right?

It says that the width is equal to 7 longer than 4 times the width, so the length is:
L = 4W + 7

And that the perimeter is 494 yards. The perimeter for a rectangle is:

P = 2L + 2W, and since we know L and P, we can plug them in, like so:

494 yards = 2(4W+7) + 2W.

Now we solve for W.

494 yards = (8W + 14) + 2W which is equal to 10W + 14.

494 yards = 10W + 14 (subtract the 14 across and divide by ten and we'll get the width!)

W = 48.

Now we know that L = 4W+7, and W = 48, so L = 4(48) + 7 = 192+ 7 = 199

so the length is 199 yards and the width is 48 yards.

You can verify this by using the perimeter formula to see if 494 = 2(48) + 2(199)

and it does.

Hope this helps!

Answer 2

Sorry that the rectangle got messed up! It didn't print the spacing properly, haha.