Math, asked by mgranandhi821, 1 year ago

The sum of length breadth and depth is19 cm and the length of its diagonal is 11 cm find the surface area of the cuboid

Answers

Answered by pinkirahangdale0
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Answered by Anonymous
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Given:

  • The sum of the length, breadth and depth of a cuboid is 19 cm.

  • The length of diagonal = 11 cm.

To find out:

Find the Surface area of the cuboid

Solution:

Let the length, breadth and height of the cuboid be l cm, b cm, h cm respectively.

✪According to question:-

l + b + h = 19 .........( i )

Now,

Diagonal of cuboid = 11 cm

⇒ √ l² + b² + h² = 11

Squaring both sides

⇒ l² + b² + h² = 121 ........( ii)

Now,

l + b + h = 19

Squaring both sides

⇒ ( l + b + h )² = ( 19 )²

[ (a + b + c)³ = a² + b² + c² + 2(ab + bc + ca) ]

⇒ l² + b² + h² + 2( lb + bh + hl ) = 361

⇒ 121 + 2 ( lb + bh + hl ) = 361

⇒ 2 ( lb + bh + hl) = 240 cm²

⇒ Surface area of cuboid = 240 cm²

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