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?

The correct answer is: 67.298

We are given that l + b + h =  5 √3 cm
And, diagonal length = 
Squaring both sides we get, l² + b² + c² = 45
Surface area of the cuboid =2(lb + bh + lh)
We know that a² + b² + c² = (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 - (l²+ b²+ h²)

= (5 √3)² – 45

= 75 – 45

= 30