KVPY SA Exam 2018 Question Paper

${\left(\mathit{a}-8\right)}^2-{\left(\mathit{b}-7\right)}^2=5$
$\left(\mathit{a}-\mathit{b}-1\right)\left(\mathit{a}+\mathit{b}-15\right)=5$
$\begin{array}{cc}{\mathrm{I}}_1& {\mathrm{I}}_2\\ \mathrm{Four}\mathrm{cases}\\ {\mathrm{I}}_1& {\mathrm{I}}_2\\ 5& 1\\ 1& 5\\ -5& -1\\ -1& -5\end{array}$
Case-1
a – b – 1 = 5 & a + b – 15 = 1
⇒ a = 11, b = 5
Case-2
a – b – 1 = –5 & a + b – 15 = –1
⇒ a = 5, b = 9
Case-3
a – b – 1 = 1 & a + b – 15 = 5
⇒ a = 11, b = 9
Case-4
a – b – 1 = –1 & a + b – 15 = –5
⇒ a = 5, b = 5 Perimeter = 4 + 4 + 6 + 6 = 20