Question

the dimensions of a cuboid are in the ratio 2 : 3 : 4 .its total surface area is 1872 cm square find its dimensions?

Answer 1

2(6x^2 +12X^2 + 8x^2)=1872
26x^2=1872
X^2=72
X=72^1/2
X=8.4852

Answer 2

Its dimensions are 12 cm , 18 cm and 24 cm

Step-by-step explanation:

We are given that the dimensions of a cuboid are in the ratio 2 : 3 : 4

Let the ratio be x

Length = 2x

Breadth = 3x

Height = 4x

Total surface area of cuboid = $2(lb+bh+hl)=2(2x \times 3x+3x \times 4x+4x \times 2x)$

We are given that its total surface area is 1872 cm square

So,$2(2x \times 3x+3x \times 4x+4x \times 2x)=1872$

$2(6x^2+12x^2+8x^2)=1872$

$6x^2+12x^2+8x^2=\frac{1872}{2}$

$26x^2=936$

$x=\sqrt{\frac{936}{26}}$

x=6

Length = 2x =2(6)=12 cm

Breadth = 3x =3(6)=18 cm

Height = 4x =4(6)=24 cm

Hence Its dimensions are 12 cm , 18 cm and 24 cm

#Learn more:

Find the total surface area of this cuboid 4cm 2cm 5cm

https://brainly.in/question/9177338