A rectangle’s length is 2 more than 3 times its width.[continue below]?

Question

If its length is decreased by 7 and its width is increased by 5, a square is formed. How long is the rectangle?

Answer 1

First break this down into 2 mathematical equations:

First equation:

L = 3W + 2 (the length is 2 more than 3 times the width)

Second equation:

L - 7 = W + 5 (length decreased by 7 equals the width increased by 5)

So we have 2 equations and 2 unknowns - substitute one into the other to give you:

L = 17

W = 5

Therefore the length is 17.

Answer 2

Let the width of the rectangle be x, and then the length would be 2+3x since it is 2 more than 3 times.

The width of the square is x + 5, since you increase it by 5, and the length is 2+3x-7 since you decrease it's length by 7.

But a squares width and length are the same, hence:

2+3x-7 = x+5

3x-5= x+5

2x = 10

x = 5

Now to find how long the rectangle is, simply sub x = 5 into the previous rectangles length, which was 2+3x.

Therefore the length of the rectange is 17 units.

Answer 3

We know:

L = 3W+2

and

L-7 = W+5

Solve for L:

W = L-12

L = 3(L-12) + 2

L = 3L -36 + 2

2L = 34

L = 17  (and, as a check, W = 5, which checks out).