Question

the sum of the l b and H of a cuboid is 17 cm and length of its diagonal is 13 cm calculate surface area

Answer 1

Let the length, breath and height of the cuboid be l, b and h respectively.

Given, l + b + h = 17cm ...(1)

Length of diagonal of the cuboid =
root over l2 + b2+ h2
root over l2+b2 +h2=13 cm


Squaring on both sides, we get

l 2 + b 2 = h 2 = 169cm2 ...(2)

Now, (l + b + h)2 = l 2 + b 2 + h 2 + 2lb + 2bh + 2hl

∴ 2(lb + bh + hl ) = ( l + b + h)2 – (l 2 + b 2 + h 2)

⇒ 2(lb + bh + hl ) = (17cm)2 – 169cm2 =289 cm2 – 169cm2 = 289 cm2 – 169cm2 = 100cm2 (Using(1) and (2))

Surface area of the cuboid = 2(lb + bh + hl) = 240cm2

∴ Surface area of the cuboid is 100cm2.

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