The sum of the length, breadth and height of a cuboid is 12cm. The length of the diagonal is 5cm. Find the surface area of the cuboid.
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Let the length ,breadth ,height be l, b, h respectively.
Now, l + b + h = 19 CM.
Given it's diagonal = 5√5 cm.
Diagonal = √ l² + b² + h² = 5√5
125 = l² + b² + h²
Also, T. S. A = 2(lb+bh+hl)
Now, Take l + b + h = 19
Squaring on both sides
(l + b + h) ² = 19²
l² + b ² + h² + 2 ( lb+ bh+hl) = 361
125 + TSA = 361
TSA = 236 cm²
Therefore, T. S. A = 236 cm²
Now, l + b + h = 19 CM.
Given it's diagonal = 5√5 cm.
Diagonal = √ l² + b² + h² = 5√5
125 = l² + b² + h²
Also, T. S. A = 2(lb+bh+hl)
Now, Take l + b + h = 19
Squaring on both sides
(l + b + h) ² = 19²
l² + b ² + h² + 2 ( lb+ bh+hl) = 361
125 + TSA = 361
TSA = 236 cm²
Therefore, T. S. A = 236 cm²
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