Let and be integers satisfying 0 < < .Let P ( , ),Q be the reflec… - Vidyadip

MCQ

Let $\alpha $ and $\beta $ be integers satisfying $0 < \beta < \alpha $ .Let $P\left( {\alpha ,\beta } \right),Q$ be the reflection of $P$ in the line $y = x, R$ be the reflection of $Q$ in the $y-$ axis, $S$ be the reflection of $R$ in the $x-$ axis and $T$ be the reflection of $S$ in the $y-$ axis. If the area of convex pentagon $PQRST$ is $187\ sq. units$ , then value of $\alpha + {\beta ^2}$ is

A
$20$
B
$34$
C
$27$
✓
$15$

✓

Answer

Correct option: D.

$15$

d
$\mathrm{P}(\alpha, \beta), Q(\beta, \alpha), R(-\beta, \alpha), S(-\beta,-\alpha), T(\beta,-\alpha)$

$187=4 \alpha \beta+\frac{1}{2} \cdot 2 \alpha(\alpha-\beta)$

$187=\alpha(\alpha+3 \beta)$

$\alpha=11,3 \beta+\alpha=17$

$\alpha=11$ and $\beta=2$

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