Chapter 11.1, Problem 24PPS

To determine

To Find: To find the base and height of the given parallelogram.

Answer to Problem 24PPS

The answer is 13mm and 17mm.

Explanation of Solution

Given information: Given area of parallelogram is 221square mm.

Formula used: Area of parallelogram $=\text{base}\times \text{height}$

Calculation:

Let the base of the parallelogram is x then, height is $(x+4)\text{mm}$

According to question.

  $\begin{array}{l}221=x\times (x+4)\\ 221=x^2+4x\\ x^2+4x-221=0\end{array}$

Using quadratic formula

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-4\pm \sqrt{4^2-4\times 1\times (-221)}}{2\times 1}\\ x=\frac{-4\pm \sqrt{16+884}}{2}\\ x=\frac{-4\pm \sqrt{900}}{2}\\ x=\frac{-4\pm 30}{2}\\ x=\frac{-4+30}{2}\text{or}x=\frac{-4-30}{2}\\ x=13\text{or}x=-17\end{array}$

Since side cannot be negative.

  $\therefore x=13$

Thus, the required base is 13mm

And the height is $13+4=17\text{mm}$

Hence, the required base and height of the parallelogram is 13mm and 17mm.