The length of a rectangle is 6 in longer than its width. If the perimeter of the rectangle is 64 in, find its length and width.

Answer 1

When facing algebra questions like this, it is always important to come up with an equation!

Let's say that the width of the rectangle is "x" and the length of the rectangle is 6 inches longer than its width, which means the length can be represented as "x + 6" inches.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2(length + width) or 2(l+w)

Substituting the given values:

64 = 2(x + 6 + x)

Simplifying the equation:

64 = 2(2x + 6)

64 = 4x + 12

Now, let's solve for "x":

4x = 64 - 12

4x = 52

x = 52 / 4

x = 13

So, the width of the rectangle is 13 inches.

Now, we can find the length by adding 6 inches to the width:

Length = x + 6 = 13 + 6 = 19 inches

Therefore, the length of the rectangle is 19 inches and the width is 13 inches.

Answer 2

The formula for perimeter of a parallelogram is P = 2L + 2W. Since we know the length is 6 inches longer than the width, we can say L = W + 6. We'll substitute W + 6 in for L in our equation.

That gives us 64 = 2(W + 6) + 2W

Distribute: 64 = 2W + 12 + 2W

Combine like terms: 64 = 4W + 12

Subtract 12 and then divide by 4: W = 13 inches

We know the length is 6 more than the width, so L = 6 + 13, so L = 19 inches

Check: 64 = 2(19) + 2(13) → 64 = 38 + 36 → 64 = 64.