The whole surface area of a rectangular block is 8788 sq

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The whole surface area of a rectangular block is 8788 sq cm. If length, breadth and height are in ratio of 4 : 3 : 2, then find the length. ?

1. 26 cm
2. 52 cm
3. 104 cm
4. 13 cm

Correct Option: B

Let length, breadth and height be 4k, 3k and 2k, respectively.
Whole surface area = 2(lb + bh + lh)
⇒ (lb + bh + lh) = 8788/2 = 4394
⇒ (4 x 3 + 3 x 2 + 2 x 4 ) k² = 4394
⇒ 26k² = 4394
⇒ k² = 169
⇒ k = 13
∴ Length = 4k = 4 x 13 = 52 cm