Use the quadratic formula to determine the exact solutions to the equation. 2x2−9x+1=0

x=9±73√4

x=−9±89√4

x=9±73√2

x=9±89√2

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!