Need help finding dimensions of rectangle

Question

The perimeter of a rectangle is 10m. Twice the width is equal to one-half the length. Find the length and width.

Answer 1

2*w = 1/2 * L <--- twice the width equals half the length

4w = L <-- multiplies both sides by 2.

P = 2L + 2w

10 = 2(4w) + 2w

10 = 8w + 2w

10 = 10w

w=1

width is 1m, length is 4m

Answer 2

Perimeter means the whole way around whatever we're talking about. Since it's a rectangle, this means going the width, then length, then width, then length again to get all the way around. This means we're doing the length twice and the width twice. If we call length L and width W, we have a formula for the perimeter:

2 * W + 2 * L = 10 m

Now we are told that twice the width is equal to one-half the length. Then

2 * W = 1/2 * L

We can substitute 2 * W = 1/2 * L into the first equation:

1/2 * L + 2 * L = 10 m

So simplifying:

2.5 * L = 10 m

If we divide by 2.5 on each side, L = 4 m. So we have one of our dimensions. We can use this dimension to find the other using the first equation:

2 * W + 2 * L = 10 m

Plugging 4 m into the equation for L:

2 * W + 2 * 4 m = 10 m

Since 2 * 4 m = 8 m, we simply subtract this from both sides, arriving at

2 * W = 2 m

Dividing both sides by 2, we arrive at

W = 1 m

So our dimensions are:

W = 1m

L = 4m