Question

The surface area of a cuboid is 1372 ${cm}^2$. If its dimensions (l : b : h) are in the ratio 4 : 2 : 1, then find the length of the cuboid (in cm).

Answer 1

Surface Area of the cuboid = 1372 ${cm}^2$. (Given)

Let length, breadth and height be l, b and h respectively

=> 2(l × b + b × h + l × h) = 1372 ${cm}^2$.

Since, it is given that

l : b : h = 4 : 2 : 1

Let l = 4k, b = 2k and h = k

therefore 2 (4k × 2k + 2k × k +4k × k) = 1372

=> 28 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $k^2$ = 1372

=> <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $k^2$ = 49

=> k = 7

therefore l = 4k = 4 × 7 = 28 cm