Question

The length of a rectangle is 16 feet more than three times the width. The perimeter of the rectangle is 248 feet. Find the dimensions of the rectangle.

Answer 1

Answer:

L = 97, w = 27

Step-by-step explanation:

The perimeter formula is P = 2L + 2w.  We have too many unknowns simply to plug in, so we have to find a way to identify one in terms of the other.  The statement is that the length is 16 feet more than 3 times the width, so the length is in terms of the width and can be identified as

L = 3w + 16

and the width, then, is just w.  Now we can fill in those 2 values, both in terms of w, and set it to equal the perimeter value we were given of 248:

2(3w + 16) + 2w = 248 and

6w + 32 + 2w = 248 and

8w + 32 = 248 and

8w = 216 so

w = 27

That means that the width is 27.  Use that value of w now to find the length where

L = 3w + 16.

L = 3(27) + 16 and

L = 97