Question

the length breadth and hight of cuboid are in the ratio 5: 4: 2. if the total surface area is 1216cm, find the dimensions of the cuboid give me the plees answer
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Answer 1

Step-by-step explanation:

let the length of cuboid is 5x

width of cuboid is 4x

height of cuboid is 2x

now surface area of cuboid is

2 [length •width +width•height + height•length ]

so put the values.

2[ 5x × 4x +4x × 2x + 2x × 5x]

2 [38 x^2]

76x^2

according to que this is equal to 1216cm^2

means. 76 x^2 = 1216cm^2

x= 4cm

now put the value of x in our assumption

length is 5 •4 is 20 cm

width is. 4 •4 is 16cm

height is 2•4 is 8cm

Answer 2

Given:

• Length,breadth and height of cuboid are in the ratio 5:4:2.
• The total surface area of cuboid is 1216cm.

To Find:

• The dimension of the cuboid.

Formula Required:

$\boxed{ \frak{Total \: surface \: area(TSA) \: of \: cuboid= 2(l×b + b×h + h×l)}} \color{navy}\bigstar$

Solution:

• Let the dimensions be 5x:4x :2x respectively.

Then,

$\begin{gathered} \bf{ \dag} \: \underline{\frak{ \color{green}{Putting \: values \: in \: given \: formula}}} \\ \\ \\ :\implies\sf{1216=2(5x\;\times\;4x\; + \;4x\;\times\;2x\;+\;2x\;\times\;5x)}\\ \\ \\ :\implies\sf{1216=2(20x^2+8x^2+10x^2)}\\ \\ \\ :\implies\sf{1216=2\times38x^2}\\ \\ \\ : \implies\sf{\frac{\cancel{1216}}{\cancel{2}}=38x^2}\\ \\ \\ :\implies\sf{608=38x^2}\\ \\ \\ :\implies\sf{x^2=\frac{\cancel{608}}{\cancel{38}}}\\ \\ \\ :\implies\sf{x=\sqrt{16}}\\ \\ \\ :\implies\underline{\boxed{\mathfrak{x=4}}}\pink\bigstar\\ \\ \\\end{gathered}$

Therefore,

• Length = 5x = 5(4) = 20cm
• Breadth = 4x = 4(4) = 16cm
• Height = 2x = 2(4) = 8cm

$\underline{\sf{Hence, the \: dimensions \: of \: the \: cuboid \: are \textsf{ \textbf{20 cm,16 cm and 8 cm}}}.}$

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