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
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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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