Math. Finding the dimensions of the Perimeter of a Rectangle..

Hi. I need help coming up with the solution for the problem below. Answer is already given.

1. The length of a rectangle is 15 meters longer than three times the width. The perimeter of the rectangle is 74 meters. Find the dimensions. Answer in fractional form using mixed numbers.

ANSWER should be: width = 5 1/2, length = 31 1/2

I know that the formula for the Perimeter of the rectangle is P = 2l + 2w. Been trying to do some computations using all the given information, but just not getting to the answer. Any help is greatly appreciated. Thanks.

So you are given:

L = 15 + 3W

and

2L + 2W = 74

substitute 1st equation for L in 2nd equation:

2(15 + 3W) +2W = 74
30 +6W +2W = 74
30 + 8W = 74
8W = 74 - 30 = 44
W = 44/8 = 5.5

back to 1st equation:

L = 15 + 3W
L = 15 + 3(5.5) = 15 + 16.5 = 31.5