Question

the length of diagonal of cuboid is 10 cm and the sum of the length , breath, height, is 14 cm then find the total surface area of cuboid​

Answer 1

$\sf \tt \: L ength \: of \: Diagonal \: of \: cuboid = \sf \: 10 \: cm \\ \: \sqrt{ \: {l \: }^{2} + b {}^{2} + h {}^{2} } = \sf \: 10 \: cm \\ \boxed{ l {}^{2} + b {}^{2} + h {}^{2} = 100}$

$\sf \: Sum \: of \: \tt \: l + b + h \sf \: = 14 \: cm$

We know

$\green{ \boxed{\red{(a + b + c) {}^{2} = \sf \: a {}^{2} + b {}^{2} + c {}^{2} + 2 \: ab + 2bc + 2ac}}}$

According to this Formula

(l+b+h) ² = l²+ b²+ h² +2lb +2 bh +2lh

$\sf(14) { }^{2} = 100 + 2(lb + bh + lh) \\ \sf \: 2(lb + bh + lh) = 14 {}^{2} - 100 \\ : \implies196 - 100 \\ \longrightarrow \green{96}$

Total Surface Area of Cuboid

= 2(lb + bh + lh)

$\implies \boxed{ \green{96 \: cm {}^{2} }}$

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