Question

the dimensions of a cuboid are in the ratio 1 :2 :3 and its lateral surface area is 72 square find its dimensions​

Answer 1

Let common among the dimensions = k

$∴$ Dimensions = k × 2k × 3k

We know,

L.S.A. of cuboid = 2h(l + b)

Also, we have - L.S.A. = 72 sq. units

According to the question:-

2 × (3k)(k + 2k) = 72

$\leadsto$ 2(3k)² = 72

$\leadsto$ 18k² = 72

$\leadsto$ k² = 4 = 2²

$\leadsto$ k = 2 units

Putting values,

Dimensions = k × 2k × 3k = 2 units × 4 units × 6 units

Answer 2

Answer:

Let length : breadth : height = 1 : 2 : 3

⇒ l =x , b = 2x , h = 3x

TSA of a cuboid = 2(lb+bh+lh)

=2(x×2x+2x×3x+x×3x)

=2(2x

2

+6x

2

+3x

2

)

88m

2

=22x

2

m

2

⇒x

2

=

22

88

m

2

m

2

∴x=±2

So the dimensions are 2×4×6

Step-by-step explanation:

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