Question

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!

Answer 1

Let's assume that length be L and width be B.

Perimeter of rectangle is given by,

Perimeter = 2( L + B)

So,

⇒ 16 cm = 2 ( L + B )

⇒ 8cm = L + B _______( Say equation 1)

Now, we are given that when length is doubled perimeter is 26.

So,

⇒ 26 cm = 2 ( 2 L + B )

⇒ 13 cm = 2 L + B

⇒ 13 cm = L + L + B

Now use equation-1

⇒13 cm = L + 8cm

⇒13 cm - 8 cm = L

⇒5 cm = L

Therefore length is 5cm.

Now substitute this value in equation 1

⇒L + B = 8 cm

⇒5cm + B = 8 cm

⇒B = 8 cm - 5 cm

⇒B = 3 cm

Therefore breadth is 3 cm.

Answer 2

Length is 5, width is 3.

Explanation:

The formula for the perimeter of a rectangle is:

`P=2l+2w`

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:

`16=2l+2w`

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

`26=4l+2w`

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

`16=2l+2w\\-16=-2l-2w`

Now, add the equations:

`-16=-2l-2w\\26=4l+2w`

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

`10=2l`

Divide both sides by 2:

`l=5`

So, the original length was 5.

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

`16=2(5)+2w`

Multiply:

`16=10+2w`

Subtract 10 from both sides:

`2w=6`

Divide both sides by 2:

`w=3`

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!