Question

In the given figure, the value of $x$ is, ($x$ is the side of the square)

• A. $15\sqrt{2}$
• B. $\frac{442}{\sqrt{441}}$
• C. $\frac{441}{\sqrt{440}}$
• D. $\frac{441}{\sqrt{442}}$

Answer 1

The correct option is D $\frac{441}{\sqrt{442}}$

We can write,
$20\cos \theta =x-y\cdots \left(1\right)21\cos \theta =x\cdots \left(2\right)21\sin \theta =y\cdots \left(3\right)\Rightarrow 20\cos \theta =21\cos \theta -21\sin \theta \Rightarrow \frac{20}{21}=1-\tan \theta \Rightarrow \tan \theta =\frac{1}{21}\Rightarrow \frac{y}{x}=\frac{1}{21}$
Now, in $\Delta ADE,$
$x^2+y^2={21}^2$
$\Rightarrow x^2+\frac{x^2}{{21}^2}={21}^2$

$\Rightarrow x=\frac{441}{\sqrt{442}}$