The area of a trapezium is 360 in2. If the ratio of the bases to the height is 6:10:5, find the dimensions of the trapezium.
To find the dimensions of the trapezium, we need to use the given information about the ratio of the bases to the height.
Let's assume the bases of the trapezium are represented by the lengths 6x and 10x (where x is a constant), and the height is represented by the length 5x.
The formula for finding the area of a trapezium is: Area = (1/2) x (sum of the bases) x height.
In this case, the area is given as 360 in^2, so we can plug in the known values into the formula and solve for x.
360 = (1/2) x (6x + 10x) x 5x
360 = (1/2) x (16x) x 5x
360 = 8x^2 x 5x
360 = 40x^3
Now, let's solve for x by dividing both sides of the equation by 40:
360/40 = 40x^3/40
9 = x^3
Taking the cube root of both sides:
∛9 = ∛(x^3)
x = ∛9
x ≈ 2.08 (rounded to two decimal places)
Now that we have the value of x, we can find the dimensions of the trapezium. Substituting the value of x into the bases and height:
Length of the smaller base = 6x ≈ 6(2.08) ≈ 12.5
Length of the larger base = 10x ≈ 10(2.08) ≈ 20.8
Height = 5x ≈ 5(2.08) ≈ 10.4
Therefore, the dimensions of the trapezium are approximately:
Length of the smaller base = 12.5 in
Length of the larger base = 20.8 in
Height = 10.4 in