Chapter 9: Q13. (page 482)

Find the perimeter of quadrilateral. Express it in simplest form.

Short Answer

Expert verified

Hence the perimeter of given quadrilateral is $\frac{13 x^{2} + 4 x - 9}{2 x (x^{2} - 1)}$

Step by step solution

Step 1. Write down the given information.

The given quadrilateral is shown below.

Step 2. Evaluating the perimeter of given quadrilateral.

The perimeter $(P)$ of the given quadrilateral is equal to the sum of length of its sides. Therefore, perimeter of given quadrilateral is evaluated as:

$\begin{matrix} P = \frac{4}{x^{2} - 1} + \frac{3}{2 x} + \frac{2}{x + 1} + \frac{3}{x} \\ = \frac{4}{(x - 1) (x + 1)} + \frac{3}{2 x} + \frac{2}{x + 1} + \frac{3}{x} \\ = \frac{8 x + 3 (x - 1) (x + 1) + 4 x (x - 1) + 6 (x - 1) (x + 1)}{2 x (x - 1) (x + 1)} \\ = \frac{8 x + 3 (x^{2} - 1) + 4 x^{2} - 4 x + 6 (x^{2} - 1)}{2 x (x^{2} - 1)} \\ = \frac{8 x + 3 x^{2} - 3 + 4 x^{2} - 4 x + 6 x^{2} - 6}{2 x (x^{2} - 1)} \\ = \frac{13 x^{2} + 4 x - 9}{2 x (x^{2} - 1)} \end{matrix}$

Step 3. Conclusion.

Hence the perimeter of given quadrilateral is $\frac{13 x^{2} + 4 x - 9}{2 x (x^{2} - 1)}$

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Find the perimeter of quadrilateral. Express it in simplest form.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Evaluating the perimeter of given quadrilateral.

Step 3. Conclusion.

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