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In cuboid the length of its diagonal is 5√5 and sum of its length breadth and depth is 19 than find it's TSA
Asked by manishbennalli | 01 Apr, 2020, 07:25: PM Expert Answer
Let l, b and h be the length, breadth and depth of a cuboid.
Given: l + b + h = 19 ... (i)
Also, given that the length of its diagonal is 5√5
Therefore, we have
√(l2 + b2 + h2) = 5√5
Squaring on both the sides, we have
l2 + b2 + h2 = 125 ... (ii)
Squaring equation (i),
(l + b + h)2 = 192 = 361
l2 + b2 + h2 + 2(lb+ bh + lh) = 361
From (ii),
125 + 2(lb+ bh + lh) = 361
2(lb+ bh + lh) = 361 - 125 = 236
Surface area of the cuboid = 2(lb+ bh + lh) = 236 cm2.
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