Lateral surface area of a cuboid is $486 m^{2}$ . Its breadth is $12$ m and length and height are in the ratio $5 : 3$ . Find the magnitude of difference of length and height of the cuboid.

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Solution

Breadth $= 12 m$
Length $= 5 x m$ (Let)
Height $= 3 x m$ (Let)
Lateral SA $= 2 (b h + l h)$
$= 2 (36 x + 15 x^{2})$
$30 x^{2} + 72 x = 486$
$30 x^{2} + 72 x - 486 = 0$
$x = 3$
Length-breadth $= 5 x - 3 x$
$= 2 x = 6 m$

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Lateral surface area of a cuboid is 486m2. Its breadth is 12 m and length and height are in the ratio 5:3. Find the magnitude of difference of length and height of the cuboid.

Breadth=12mLength=5xm (Let)Height=3xm (Let)Lateral SA=2(bh+lh)=2(36x+15x2)30x2+72x=48630x2+72x−486=0x=3Length-breadth=5x−3x=2x=6m

Lateral surface area of a cuboid is $486 m^{2}$ . Its breadth is $12$ m and length and height are in the ratio $5 : 3$ . Find the magnitude of difference of length and height of the cuboid.

Breadth $= 12 m$
Length $= 5 x m$ (Let)
Height $= 3 x m$ (Let)
Lateral SA $= 2 (b h + l h)$
$= 2 (36 x + 15 x^{2})$
$30 x^{2} + 72 x = 486$
$30 x^{2} + 72 x - 486 = 0$
$x = 3$
Length-breadth $= 5 x - 3 x$
$= 2 x = 6 m$