Question

the dimensions of a cuboid are in the ratio 4:3:2 and its surface area is 1872 cm2.
find its length breadth and height

Answer 1

Step-by-step explanation:

surface area = 2(l×b + l×h + h×b)

according to question,

let's ,length = 4x

breath = 3x

height = 2x

so,

2(4x×3x + 4x×2x + 2x×3x) = 1872

12x² + 8x² + 6x² = 1872/2

26x² = 936

x² = 936/26

x² = 36

x = 6 answer

so, at random

length = 24

breath = 18

height = 12

hope this is helpful for you

Answer 2

Given: Ratio of dimensions of a cuboid is 4:3:2 & The Total surface area of cuboid is 1872 cm².

To find: Length, breadth & height of cuboid?

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

☯ Let length, breadth and height of cuboid be 4x, 3x and 2x respectively.

⠀⠀⠀⠀

Now,

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

⋆ Total surface area of cuboid is given by,

$\star\;{\boxed{\sf{\pink{TSA_{\:(cuboid)} = 2(lb + bh + hl)}}}}$

where,

• l, b & h are length, breadth and height of cuboid respectively.

⠀⠀⠀⠀

$\sf We\:have \begin{cases} & \sf{Length,\:l = \bf{4x}} \\ & \sf{Breadth\:,b = \bf{3x}} \\ &\sf {Height\:,h = \bf{2x}} \\ & \sf{TSA_{\:(cuboid)} = \bf{1872\:cm^2}}\end{cases}$

$\dag\;{\underline{\frak{Putting\:values\:in\;formula,}}}$

$:\implies\sf 2(4x \times 3x + 3x \times 2x + 2x \times 4x) = 1872$

$:\implies\sf 2(12x^2 + 6x^2 + 8x^2) = 1872\\ \\ \\:\implies\sf 2(12x^2 + 14x^2) = 1872\\ \\ \\ :\implies\sf 2 \times 26x^2 = 1872\\ \\ \\ :\implies\sf 26x^2 = \cancel{ \dfrac{1872}{2}}\\ \\ \\ :\implies\sf 26x^2 = 936\\ \\ \\ :\implies\sf x^2 = \cancel{\dfrac{936}{26}}\\ \\ \\ :\implies\sf x^2 = 36\\ \\ \\ :\implies\sf \sqrt{x^2} = \sqrt{36}\\ \\ \\ :\implies\sf x = \sqrt{36}\\ \\ \\:\implies{\underline{\boxed{\frak{\purple{x = 6}}}}}\;\bigstar$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

Therefore,

⋆ The dimensions of cuboid are,

⠀⠀⠀⠀

• $\sf Length,\: 4x = 4 \times 6 = \bf{24}$

• $\sf Breadth,\: 3x = 3 \times 6 = \bf{18}$

• $\sf Height,\: 2x = 2 \times 6 = \bf{12}$

⠀⠀⠀⠀

$\therefore$ Thus, The length, breadth & height of cuboid are 24 cm, 18 cm & 12 cm respectively.