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The length of a new rectangular playing field is 4 yards longer than triple the width. If the perimeter of the rectangular playing field is 416 ​yards, what are its​ dimensions?

User Hamchapman
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Answer: Let's call the width of the rectangular playing field "w" and the length "l". From the problem, we know that:

l = 3w + 4 (the length is 4 yards longer than triple the width)

We also know that the perimeter of a rectangle is the sum of the lengths of all four sides, so:

P = 2l + 2w

We are given that the perimeter is 416 yards, so we can substitute that into the perimeter equation:

416 = 2(3w + 4) + 2w

Simplifying and solving for w:

16 = 6w + 8

8 = 6w

w = 8/6 = 4/3

We can now substitute that back into the equation for the length:

l = 3w + 4

l = 3(4/3) + 4

l = 4 + 4

l = 8

So the dimensions of the rectangular playing field are 4/3 yards wide and 8 yards long.

Explanation:

User Donzell
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