Question
Download Solution PDFThe length of a diagonal of a cuboid is 11 cm. The surface area is 240 square cm. What is the sum of its length, breadth and height ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
The diagonal of a cuboid is given by: √(L² + B² + H²)
The surface area of a cuboid is given by: 2(LB + BH + HL)
(a + b + c)² = a² + b² + c² + 2(ab + bc + ac)
Calculation:
By using the above formula
√(L² + B² + H²) = 11 cm
2(LB + BH + HL) = 240cm²
⇒ LB + BH + HL = 120cm²
We know that
(a + b + c)² = a² + b² + c² + 2(ab + bc + ac)
(L + B + H)² = 11² + 2 × 120 = 121 + 240 = 361
Taking the square root of both sides
∴ L + B + H = √361 = 19cm
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