Question

A rectangle with a perimeter of 19m^2+2m-10 and a width of m^2 write an expression for the lenght

Answer 1

Answer: $\frac{17}{2}m^2+m-5$

Step-by-step explanation:

By definition, the perimeter of a rectangle is:

$P=2l+2w$

Where "l" is the lenght and "w" is the width.

If you solve for "l":

$P-2w=2l\\\\l=\frac{P-2w}{2}$

In this case, you know that the following expression represents  the perimeter of the rectangle:

$19m^2+2m-10$

And the width of that rectanle is represented wih this expression:

$m^2$

Therefore, based on the explained above, you can conclude that the lenght  of that rectangle is given  by:

$\frac{19m^2+2m-10-2(m^2)}{2}$

Finally, simplifying the expression, you get:

$=\frac{17m^2+2m-10}{2}=\frac{17}{2}m^2+m-5$