Question

the surface area of a cuboid is 120 square metre if the length and breadth of the cuboid are equal and the height is 2 metre 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

$\tt{\rightarrow p^2+4p=\dfrac{120}{2}}$

⇒ 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

Answer 2

AnSwEr

120 m² is the Surface Area of cuboid

Formula = 2(lb + bh + lh) = 120 m²

Let L be Length and B be Breadth

= 2 ( B² + 2B + 2B ) = 120

= B2 + 4B = 2120

= B² + 4p = 60L2

= B² + 4p - 60 = 0

= B² + ( 10 - 6 ) B - 60 = 0

= B² + 10B - 6B - 60 = 0

= B ( B + 10 ) - 6 ( B + 10 ) = 0

= ( B + 10 ) ( B - 6 ) = 0

= B + 10 = 0

= B = -10

= B - 6 = 0

B = 6

Breadth = -10

Breadth = -10 This is unacceptable.

L = B = 6

Length = Breadth = 6