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