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.
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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
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