The perimeter of a rectangle is 16cm. If the length is doubled, the perimeter is 26. What are the length and width of the rectangle? Please explain all steps required, thanks ahead of time!

Length is 5, width is 3.

Step-by-step explanation:

The formula for the perimeter of a rectangle is:

Where P is the perimeter, l is the length, and w is the width.

With the original length and width, the perimeter is 16, thus:

Now, if we double the length, the 2l will become 4l. Also, the perimeter will change to 26. Thus:

Now, we have a system of equations. We can solve it using elimination. Multiply everything by -1 in the first equation:

Now, add the equations:

-16 plus 26 is 10. -2l plus 4l is 2l. The 2w cancel. Thus:

Divide both sides by 2:

So, the original length was 5.

To find the original width, substitute 5 back into the first equation:

Multiply:

Subtract 10 from both sides:

Divide both sides by 2:

So, the original width was 3.

And we're done!

Checking:

Originally, our length was 5 and 3. This means that the perimeter is 2(5+3)=2(8)=16 which is correct.

After we double our length, our length will be 10. This means that the new perimeter is 2(10+3)=2(13)=26. So, our answers are correct!

hello i am doing good for you that it's summer in your country or state ; )

btw in my country we just have sun and rain as (because i live in the caribbean lol)

also, thx a lot for the points : )

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.