Question

The dimension of a cuboid are in the ratio 7:3:2.and its tsa is 2050sqcm.find its dimensions

Answer 1

Answer::

$\red { Dimensions \:of \: the \: cuboid }$

$\green { l = 35 \:cm ,\:b= 15\:cm ,\:h = 10\:cm}$

Step-by-step explanation:

Given

ratio of dimensions of a cuboid l:b:h = 7:3:2

Let l = 7x , b = 3x , h = 2x

TSA = 2050 cm² ( given)

=> 2(lb + bh + hl) = 2050

=> 2( 7x × 3x + 3x × 2x + 2x × 7x ) = 2050

=> 2( 21x² + 6x² + 14x²) = 2050

=> 2 × 41x² = 2050

=> 82x² = 2050

/* Divide both sides by 25 , we get

=> x² = 25

$\implies x = \sqrt{25}\\= 5$

$Now ,\: Dimensions \: of \: the \: cuboid \:are \\</p><p>l = 7x = 7\times 5 = 35 \:cm$

$b = 3x = 3\times 5 = 15\:cm \\h = 2x = 2\times 5 = 10\:cm$

Therefore.,

$\red { Dimensions \:of \: the \: cuboid }$

$\green { l = 35 \:cm ,\:b= 15\:cm ,\:h = 10\:cm}$

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