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The sum of length, breadth and height of a cuboid is x cm and length of its diagonal is y cm, then its…

Let dimensions be \(l, b, h\). Given \(l+b+h = x\) and diagonal \(\sqrt{l^2+b^2+h^2} = y \implies l^2+b^2+h^2 = y^2\). Total surface area \(= 2(lb+bh+hl) = (l+b+h)^2 -…

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The sum of length, breadth and height of a cuboid is x cm and length of its diagonal is y cm, then its complete surface area will be-

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Correct answer A

Let dimensions be l,b,hl, b, h. Given l+b+h=xl+b+h = x and diagonal l2+b2+h2=y  ⟹  l2+b2+h2=y2\sqrt{l^2+b^2+h^2} = y \implies l^2+b^2+h^2 = y^2. Total surface area =2(lb+bh+hl)=(l+b+h)2−(l2+b2+h2)=x2−y2= 2(lb+bh+hl) = (l+b+h)^2 - (l^2+b^2+h^2) = x^2 - y^2.

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