Question

The surface area of a cuboid is 1372 sq cm if its dimensions are in ratio 4:2:1, find them

Answer 1

Let the length be 4x
Let the breadth be 2x
Let the height be x

Surface area=2(lb+bh+hl)
=2(8x²+2x²+4x²)
=28x²=1372
so x²=49
and x=7

So length=4x=28cm
breadth=2x=14cm
&. height=x=7cm

I hope the above solution will help you...

Answer 2

Given - Surface area = 1372 cm²

Ratio of dimensions = 4:2:1

Find - Dimensions of cuboid.

Solution = Surface area of cuboid is given by the formula = 2(length*breadth + breadth*height + height* length).

Now, let us say that length of each dimension is 4x, 2x and 1x. Keeping these values in the formula mentioned above, we can calculate surface area of cuboid.

Surface area of cuboid = 2(4x*2x + 2x*1x + 1x*4x)

1372 = 2(8x² + 2x² + 4x²)

1372 = 2(14x²)

686 = 14x²

x² = 686/14

x² = 49

x = ✓49

x = 7 centimetres

Hence, calculating dimensions of cuboid.

4x = 4*7

28 centimetres

2x = 2*7

14 centimetres

1x = 1*7

7 centimetres

Therefore, dimensions of given cuboid is 28, 14 and 7 centimetres