Question
The area of a trapezium is 400 cm squared the sides and height are in terms of x when the height of data prism if the top part is 13x CM and height is 5x cm and about is 17x cm and the other but closer to the underpart is 10x cm
Answers
GPT 3.5
To find the area of a trapezium, we use the formula:
Area = (1/2) * (sum of parallel sides) * height
Given that the area of the trapezium is 400 cm^2, the height is 5x cm, and the lengths of the top and bottom sides are 13x cm and 17x cm respectively.
So we have:
400 = (1/2) * (13x + 17x) * 5x
400 = (1/2) * 30x * 5x
400 = 75x^2
x^2 = 400/75
x^2 = 16/3
x = √(16/3)
x = 4/√3
x = (4√3)/3
Therefore, the value of x is (4√3)/3.
Now, we can calculate the heights of the prism using the given lengths in terms of x:
Height of the top part = 13x = 13 * (4√3)/3 = 52√3/3 cm
Height of the bottom part = 17x = 17 * (4√3)/3 = 68√3/3 cm
Height of the prism = 5x = 5 * (4√3)/3 = 20√3/3 cm
So, the height of the prism is 20√3/3 cm.
Area = (1/2) * (sum of parallel sides) * height
Given that the area of the trapezium is 400 cm^2, the height is 5x cm, and the lengths of the top and bottom sides are 13x cm and 17x cm respectively.
So we have:
400 = (1/2) * (13x + 17x) * 5x
400 = (1/2) * 30x * 5x
400 = 75x^2
x^2 = 400/75
x^2 = 16/3
x = √(16/3)
x = 4/√3
x = (4√3)/3
Therefore, the value of x is (4√3)/3.
Now, we can calculate the heights of the prism using the given lengths in terms of x:
Height of the top part = 13x = 13 * (4√3)/3 = 52√3/3 cm
Height of the bottom part = 17x = 17 * (4√3)/3 = 68√3/3 cm
Height of the prism = 5x = 5 * (4√3)/3 = 20√3/3 cm
So, the height of the prism is 20√3/3 cm.