The lateral surface area of a cuboid is $300$ sq.cm the ratio of Length, breadth and height are in the ratio $4 : 2 : 1$ find the Length, breadth and height of the cubiod

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Solution

Let the length , breadth and height of a cuboid be $4 x, 2 x$ and $x$ respectively.
Lateral Surface area of the cuboid $= 2 (b h + l h)$
$\Rightarrow 300 = 2 (b + l) h$
$\Rightarrow 300 = 2 (2 x + 4 x) x$
$\Rightarrow 12 x^{2} = 300$
$\Rightarrow x^{2} = \frac{300}{12} = 25$
$∴ x = 5$ cm
Hence length $= 4 x = 4 \times 5 = 20$ cm, Breadth $= 2 x = 2 \times 5 = 10$ cm and height $= x = 5$ cm

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The lateral surface area of a cuboid is 300 sq.cm the ratio of Length, breadth and height are in the ratio 4:2:1 find the Length, breadth and height of the cubiod

Let the length , breadth and height of a cuboid be 4x,2x and x respectively.Lateral Surface area of the cuboid=2(bh+lh)⇒300=2(b+l)h⇒300=2(2x+4x)x⇒12x2=300⇒x2=30012=25∴x=5cmHence length=4x=4×5=20cm, Breadth=2x=2×5=10cm and height=x=5cm

The lateral surface area of a cuboid is $300$ sq.cm the ratio of Length, breadth and height are in the ratio $4 : 2 : 1$ find the Length, breadth and height of the cubiod