Question

5. The total surface area of a cuboid is 120 sq. m. If the length and breadth of the cuboid are equal and the height is 2 m, find the length and breadth.​

Answer 1

Surface Area of cuboid

= 120 m²

Using Formula

⇒ 2(lb + bh + lh) = 120 m²

Assumption

Length = p

Also

Breadth = p

Situation would be like

⇒ 2(p² + 2p + 2p) = 120

⇒ p² + 4p = 60m²

⇒ p² + 4p - 60 = 0

Splitting the middle term

⇒ p² + (10 - 6)p - 60 = 0

⇒ p² + 10p - 6p - 60 = 0

⇒ p(p + 10) - 6(p + 10) = 0

⇒ (p + 10)(p - 6) = 0

⇒ p + 10 = 0

⇒ p = -10

⇒ p - 6 = 0

⇒ p = 6

p = -10 is not acceptable

Hence

Length = Breadth = 6