Question

Construct a rectangle $WXYZ$ in which $WX=7$ cm and $XY=4$ cm. Find the length of its diagonal.

• A. $\sqrt{65}$ cm
• B. $\sqrt{64}$ cm
• C. $\sqrt{56}$ cm
• D. None of these

Answer 1

The correct option is A $\sqrt{65}$ cm

$\Rightarrow$ Draw a line segment $WX=7cm$

$\Rightarrow$ Construct an angle of ${90}^{\circ }$ at points $W$ and $X$.

$\Rightarrow$ Cut off $WZ=4cm$ and $XY=4cm$

$\Rightarrow$ Join $YZ$ and $WY$

$\Rightarrow$ Thus, $WXYZ$ is a required rectangle.

$\Rightarrow$ We know that all four angles in rectangle is ${90}^{\circ }$.

$\Rightarrow$ In right angled $△WXY$

$\Rightarrow$ $W{Y}^2=W{X}^2+X{Y}^2$ [Pythagoras theorem]

$\Rightarrow$ $W{Y}^2=7^2+4^2$

$\Rightarrow$ $W{Y}^2=49+16$

$\Rightarrow$ $W{Y}^2=65$

$\Rightarrow$ $WY=\sqrt{65}cm$

$\therefore$ Length of diagonal is $\sqrt{65}cm$