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the surface area of a cuboid is 1372c * m ^ 2 . if its dimensions are in the ratio 4 * 2 * 1 , find its length

User Serefbilge
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Answer:

Explanation:

Let's denote the dimensions of the cuboid as length (L), width (W), and height (H). According to the given information, the dimensions are in the ratio 4:2:1. We can represent this as:

L : W : H = 4 : 2 : 1

To find the length of the cuboid, we'll assign a common multiplier to each part of the ratio. Let's assume the common multiplier is x:

L = 4x

W = 2x

H = x

The surface area (SA) of a cuboid is given by the formula:

SA = 2(LW + LH + WH)

Substituting the values we obtained:

1372 = 2(4x * 2x + 4x * x + 2x * x)

1372 = 2(8x^2 + 4x^2 + 2x^2)

1372 = 2(14x^2)

1372 = 28x^2

Now we can solve for x:

28x^2 = 1372c * m^2

x^2 = (1372) / 28

x^2 = 49

Taking the square root of both sides:

x = √(49)

x = 7

Now that we have the value of x, we can find the length (L) by substituting it into the expression L = 4x:

L = 28

Therefore, the length of the cuboid is 28

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