Answer:
Length is 5, width is 3.
Step-by-step explanation:
The formula for the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
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:
[tex]16=2l+2w[/tex]
Now, if we double the length, the 2l will become 4l. Also, the perimeter will change to 26. Thus:
[tex]26=4l+2w[/tex]
Now, we have a system of equations. We can solve it using elimination. Multiply everything by -1 in the first equation:
[tex]16=2l+2w\\-16=-2l-2w[/tex]
Now, add the equations:
[tex]-16=-2l-2w\\26=4l+2w[/tex]
-16 plus 26 is 10. -2l plus 4l is 2l. The 2w cancel. Thus:
[tex]10=2l[/tex]
Divide both sides by 2:
[tex]l=5[/tex]
So, the original length was 5.
To find the original width, substitute 5 back into the first equation:
[tex]16=2(5)+2w[/tex]
Multiply:
[tex]16=10+2w[/tex]
Subtract 10 from both sides:
[tex]2w=6[/tex]
Divide both sides by 2:
[tex]w=3[/tex]
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!
