Question

which of the following words would correctly decode the word zhofrph if the simple alphabet shifting code is used​

Answer 1

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?

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

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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.

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

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

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

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

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Therefore,

⋆ The dimensions of cuboid are,

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

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

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

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