Question

Area of a rectangle is 160 cm².if the length is decreased by 4cm and breadth is increased by 2cm it becomes a square . find length and breadth

Answer 1

$let \: \: length \: \: be \: \: \: l \\ then \: \: breadth \: \: is \: \: \frac{160}{l} \\ after \: \: change \: \: in \: \: dimensions \\ l - 4 = \frac{160}{l} + 2 \\ l(l - 4) = 160 + 2l \\ {l}^{2} - 6l - 160 = 0 \\ (l - 16)(l + 10) = 0 \\ l = 16 \: \: or \: \: - 10 \\ since \: \: - ve \: \: for \: \: l \: \: is \: \: not \: \: admissible \\ length = 16 \\ breadth = \frac{160}{16} = 10$