Question

Area of rectangular is 24square cemeteries and perimeter is 20 cm then length of diagonal is

Answer 1

$l \times b = 24 \\ \\ 2(l + b ) = 20 \\ l + b = 10 \\ b = 10 - l$
$l \times (10 - l) = 24$
$- {l}^{2} + 10l = 24$
${l}^{2} - 10l + 24 = 0$
${l}^{2} - 4l - 6l + 24 = 0$
$l(l - 4) - 6(l - 4) = 0$
$l =4 \\ l = 6$
$b = 10 - 6$
$b = 4$

$d = \sqrt{ {l}^{2} + {b}^{2} }$
$= \sqrt{36 + 16}$
$= \sqrt{52}$
$= 2 \sqrt{13}$