SOLUTION: The length of a rectangle is 6 inches less than 3 times the width. The perimeter is 28 inches. Find the length and the width

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Question 1146620: The length of a rectangle is 6 inches less than 3 times the width. The perimeter is 28 inches. Find the length and the width
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
dimensions x and 3x-6

x%2B%283x-6%29=28%2F2
-
4x-6=14
4x=20
x=5

.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) The perimeter is twice the length plus twice the width: P+=+2l%2B2w

(2) The length is 6 inches less than 3 times the width: l+=+3w-6

Substitute (2) in (1): P+=+2%283w-6%29%2B2w

(3) The perimeter is given as 28 inches: 28+=+2%283w-6%29%2B2w

Solve that equation for the width w using basic algebra; then use (2) to find the length.

That's a good solution using formal algebra; and using the formal algebra to find the solution is good practice.

But if a formal algebraic solution is not required, guess and check is the fastest way to the answer. The perimeter is 28 inches, so length plus width is 14 inches.

Try combinations of length and width with a sum of 14 and find which pair satisfies the condition that the length is 6 less than 3 times the width:

1 and 13: 3(1)-6 = -3 nonsense
2 and 12: 3(2)-6 = 0 no...
3 and 11: 3(3)-6 = 3 no...
4 and 10: 3(4)-6 = 6 no...
5 and 9: 3(5)-6= 9 YES! DONE.