Question

The surface area of a cuboid is 120sq .cm. if the length and breadth of the cuboid are equal and the height is 2m.find the length and breadth​

Answer 1

$2( lb+ bh + lh ) = 120 {cm}^{2} \\ lb + bh + hl = 60 {cm}^{2}$

Here, Let the length & breadth be n.

${n}^{2} + 2n + 2n = 60 \\ {n}^{2} + 4n = 60 \\ {n}^{2} + 4n - 60 = 0 \\ {n}^{2} + (10 - 6)n - 60 = 0 \\ {n}^{2} + 10n - 6n - 60 = 0 \\ n( n+ 10) - 6(n + 10) = 0 \\ (n + 10)(n - 6) = 0$

Hence, the value of n is 6.
Therefore, length & breadth is 6 cm