The sum of length, breadth and depth of a cuboid is 19 cm

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The sum of length, breadth and depth of a cuboid is 19 cm and its diagonal is 5√5 cm. Its surface area would be ?

1. 361 m²
2. 125 m²
3. 246 m²
4. 486 m²

Correct Option: C

L + B + H = 19 cm, where L is the length, B is the breadth and
H is the height of the cuboid.
∴ (√L² + B² + H²
= (5√5)
On squaring both sides, we get
L² + B² + H² + = 125
(L + B + H)² = L² + B² + H² + 2LB + 2LH + 2BH
⇒ (19)² = 125 + 2(LB + LH + BH)
∴ Surface area = 2(LB + LH + BH)
= 19² = 125 + 2(LB + LH + BH)
= 19² - 125 = 361 - 125 = 19² - 125
= 361 - 125 = 236 cm²