Q13. Find the perimeter of quadrilate... [FREE SOLUTION]

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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 $\frac{13 x^{2} + 4 x 鈭� 9}{2 x (x^{2} 鈭� 1)}$

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:

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