Gujarat BoardEnglish MediumSTD 8MATHSUnderstanding Quadrilaterals1 Mark
MCQ
Tick the correct answer in the following? A polygon has $27$ diagonals. How many sides does it have?
A
$7$
B
$8$
✓
$9$
D
$12$
✓
Answer
Correct option: C.
$9$
$\frac{\text{n}(\text{n}-3)}{2}=27$
$\Rightarrow(\text{n}-3)=54$
$\Rightarrow\text{n}^2-3\text{n}-54=0$
$\Rightarrow\text{n}^2-9\text{n}+6\text{n}-54=0$
$\Rightarrow\text{n}(\text{n}-9)+6(\text{n}-9)=0$
$\Rightarrow\text{n}=-6\ \text{or}\ \text{n}=9$
Number of sides cannot be negative.
$\therefore\text{n}=9$
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