Question

if the Length, breadth and height of a cuboid are in ratio 5:4:3 and its total surface area is 376 square metre find its dimensions

Answer 1

$2(5x \times 4x + 4x \times 3x + 3x \times 5x) = 376 \\ 2(20x {}^{2} + 12x {}^{2} + 15 {}^{2} ) = 376 \\ 2 \times 47x {}^{2} = 376 \\ 47x {}^{2} = \frac{376}{2} \\ 47x {}^{2} = 188 \\ x {}^{2} = \frac{188}{47} \\ x {}^{2} = 4 \\ x = \sqrt{4} \\ x = 2 \\ dimensions \\ length = 5x = 5 \times 2 = 10m \\ breadth = 4x = 4 \times 2 = 8m \\ height = 3x = 3 \times 2 = 6m$

Answer 2

Answer:

10 √6 cm

Step-by-step explanation:

surface area of cuboid = 376 cm^2

the ratio of length , breadth , height of cuboid = 5 : 4 : 3

SA of cuboid = 2 ( lb + bh + lh )

diagonal of cuboid = √ ( l^2 + b^2 + h^2 )

diagonal of cube = a√3

let the length breadth height be 5x , 4x , 3x

= 2 ( (5x * 4x) + (4x * 3x) + (5x * 3x ) ) = 376

= 2 ( 20x^2 + 12x^2 + 15x^2 ) = 376

=  x =2

length = 10 cm

breadth = 8 cm

height = 6 cm

main diagonal of the cuboid = √ ( 10^2 + 8^2 + 6^2 )

                                               = 10 √2 cm

the side of cube = 10 √2 cm

main diagonal of the cube = 10 √2 * √3

                                            = 10 √6 cm