Question-156789

Question Number 156789 by cortano last updated on 15/Oct/21

Commented by john_santu last updated on 15/Oct/21

l e t A B = a; A M = C N = a - R

\Rightarrow 65 = 23 + 2 (a - R)

\Rightarrow 42 = 2 (a - R)

\Rightarrow 21 = a - R

l e t A D = b

\Rightarrow b - R = 23 + A M

\Rightarrow b - R = 23 + a - R

\Rightarrow b = 23 + a

\Rightarrow 65^{2} = a^{2} + {(23 + a)}^{2}

\Rightarrow 4225 = 2 a^{2} + 46 a + 529

\Rightarrow 2 a^{2} + 46 a - 3696 = 0

\Rightarrow a^{2} + 23 a - 1848 = 0

\Rightarrow (a - 33) (a + 56) = 0

\Rightarrow {\begin{cases} a = 33 \\ b = 56 \end{cases} \Rightarrow a r e a o f A B C D = 1848 {c m}^{2}