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1. If the diagonal and the area of a rectangle are 25 m² and 168 m², what is the length of the rectangle ?

A. 12 m

B. 17 m

C. 24 m

D. 31 m

Solution:

Let the length of the rectangle be x metres.
Then, breath of the rectangle =

(\frac{168}{x}) m

\begin{aligned} ∴ \sqrt{x^{2} + {(\frac{168}{x})}^{2}} = 25 \\ \Rightarrow \sqrt{x^{2} + \frac{28224}{x^{2}}} = 25 \\ \Rightarrow x^{2} + \frac{28224}{x^{2}} = 625 \\ \Rightarrow x^{4} - 625 x^{2} + 28224 = 0 \\ \Rightarrow x^{4} - 576 x^{2} - 49 x^{2} + 28224 = 0 \\ \Rightarrow x^{2} (x^{2} - 576) - 49 (x^{2} - 576) = 0 \\ \Rightarrow (x^{2} - 576) (x^{2} - 49) = 0 \\ \Rightarrow x^{2} = 576 o r x^{2} = 49 \\ \Rightarrow x = 24 o r x = 7 \end{aligned}

Hence, length = 24 m and breadth = 7 m

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