Maths-

General

Easy

Question

# Sum of length, height, and breadth of a rectangular box is 5 √3 cm and the diagonal length is 3√5 cm. Calculate the T.S.A of the rectangular box?

- 66.294
- 68.292
- 67.298
- 68.296

Hint:

** **

Let l, b, h, be the length, breadth and height of the cuboid.

## The correct answer is: 67.298

### We are given that l + b + h = 5 √3 cm

And, diagonal length =

Squaring both sides we get, l^{2} + b^{2} + c^{2} = 45

Surface area of the cuboid =2(lb + bh + lh)

We know that a^{2} + b^{2} + c^{2} = (a + b + c)^{2} - 2 (ab + bc + ca)

Comparing with the above formula, we get

Surface area of the cuboid = 2(lb + bh +lh)

= (l + b + h)^{2} - (l^{2}+ b^{2}+ h^{2})

= (5 √3)^{2} – 45

= 75 – 45

= 30

^{2}- (l

^{2}+ b

^{2}+ h

^{2})

^{2}– 45

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