Question
Find the value of x in the given rectangle ABCD.
✓
Answer
We know that in a rectangle opposite sides are equal.
$\therefore A D=B C=8 \text { and } A B=C D=15$
So, consider a $\triangle A B C$,
where, $A B=15$ and $B C=8$
Also, $\angle A B C=90^{\circ} \quad$ [angle of a rectangle is $90^{\circ}$]
By Pythagoras property, we have
$A C^2 =A B^2+B C^2 $
$\Rightarrow x^2 =15^2+8^2=225+64=289 $
$\Rightarrow x =17$
$\therefore A D=B C=8 \text { and } A B=C D=15$
So, consider a $\triangle A B C$,
where, $A B=15$ and $B C=8$
Also, $\angle A B C=90^{\circ} \quad$ [angle of a rectangle is $90^{\circ}$]
By Pythagoras property, we have
$A C^2 =A B^2+B C^2 $
$\Rightarrow x^2 =15^2+8^2=225+64=289 $
$\Rightarrow x =17$
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