Question

the sum of length, breadth and height of a cuboid is 21cm and the length of its diagonal is root 149 cm, then find the surface area of the cuboid.

Answer 1

Answer:

292 cm^2

Step-by-step explanation:

1. l + b + h = 21

2. l^2 + b^2 + h^2 = d^2 = (√149)^2

3. 2(lb + bh + hl) = Surface area of cuboid

Using the algebraic identity,

4. (l + b+ h)^2 = l^2 + b^2 + h^2 + 2(lb + bh + hl)

Squaring on both sides of equation 1.

5. (l + b + h)^2 = 441

Substituting the value of (l + b+ h)^2 and l^2 + b^2 + h^2 from equation 5. and 2. in equation 4. ,

441 = 149 + 2(lb + bh + hl)

Now from equation 3.

441 = 149 + Surface area of cuboid

Surface area of cuboid = 441 - 149 = 292 cm^2