Question

the base and height of parallelogram is (x-7)meters and (x+9)meters.if the area of a parallelogram is 92 square meters.find the actul values of its dimensions.

Answer 1

It is given that the base and height of parallelogram is (x-7)meters and (x+9)meters

The area is 92 square meters so it follows:

$\begin{gathered} (x-7)(x+9)=92 \\ x^2-7x+9x-63=92 \\ x^2+2x-155=0 \end{gathered}$

Solve the quadratic equation by the formula to get:

$\begin{gathered} x=\frac{-2\pm\sqrt[]{4-4\times-155\times1}}{2} \\ x=\frac{-2\pm\sqrt[]{624}}{2} \\ x=-1\pm2\sqrt[]{39} \end{gathered}$

Since the length is positive, the value of x is:

$x=-1+2\sqrt[]{39}$

So the value of the base and height are:

$\begin{gathered} x-7=-1+2\sqrt[]{39}-7\approx4.9 \\ x+9=-1+2\sqrt[]{39}+9\approx20.49 \end{gathered}$

Hence the base is 4.9 meters and the height is 20.49 meters.