The perimeter of a rectangle can be found using the formula P = 2l + 2w, where l is the length and w is the width.
Here is what we know of the rectangle:
P = 68 in
l = 3w - 2
To find the length, plug 68 for P into P = 2l + 2w, and plug 3w - 2 for l in the same formula. Then solve algebraically for w.
P = 2l + 2w
68 = 2(3w - 2) + 2w
68 = 6w - 4 + 2w
68 = 8w - 4
72 = 8w
9 = w
Now that we have w, we can plug it into 3w - 2 to find l, length.
3w - 2
3(9) - 2
27 - 2
25
That makes our length 25 inches and our width 9 inches. (Don't forget to write units!) Let's plug everything back into the formula to check our work.
68 = 2(25) + 2(9)
68 = 50 + 18
68 = 68 -- This is true
Answer:
The length of the rectangle is 25 inches.
