Question

In the following figure, what is the value of $x$ in terms of $y$?

• A. $10y$
• B. $10y^2$
• C. $y\sqrt{10}$
• D. $\sqrt{10y}$
• E. $10\sqrt{y}$

Answer 1

The correct option is C $y\sqrt{10}$

As per Pythagoras theorem,
hypotenuse${}^2=$ base ${}^2+$ perpendicular ${}^2$
In the given figure, $h=x,b=3y,p=y$
As per theorem, we have
$x^2={\left(3y\right)}^2+y^2$
$x=\sqrt{9y^2+y^2}$
$x=\sqrt{{10y}^2}$$=y\sqrt{10}$