The sum of the length, width, and depth of a cuboid is 8 cm and its diagonal is 5 cm. What is its surface area?

Correct option is A

Given:

l + w + h = 8 cm

Diagonal d = 5 cm

Concept Used:

Diagonal of a cuboid:

d = $$\sqrt{l^2 + w^2 + h^2}$$​​

Surface area of cuboid ,S = 2(lw + wh + hl)

Formula Used:

Use the identity:

​$$(l + w + h)^2 = l^2 + w^2 + h^2 + 2(lw + wh + hl)$$​​

Rearranged to find surface area:

​$$2(lw + wh + hl) = (l + w + h)^2 - (l^2 + w^2 + h^2)$$​​

Solution:

​$$(l + w + h)^2 = 8^2 = 64$$​​

​$$l^2 + w^2 + h^2 = d^2 = 5^2 = 25$$​​

Surface area = $$64 - 25 = 39 \, \text{cm}^2$$​​