The triangle in the trapezoid share a 15 inch base and a height of 10 inches. The area of the trapezoid is less than twice the area of the triangle. Find the values of X. X is greater than --- and x is less than 15 inches.
I don't think this is right, for my problem you have to explain....
Assuming that x is the length of the missing parallel side ...
area of trapezoid = (x+15)(10)/2= 5x + 75
area of triangle = (1/2)(15)(10) = 75
5x + 75 < 2(75)
5x < 75
x < 15
but clearly x has to be positive
0 < x < 15
looks like a common sense type of question to me.
To find the values of X, we need to set up an equation based on the given information.
Let's consider the trapezoid first. The area of a trapezoid is given by the formula:
Area = [(base1 + base2) / 2] * height
We are given that the triangle and the trapezoid share a 15-inch base and have a height of 10 inches. So, the area of the trapezoid can be expressed as:
Area of trapezoid = [(15 + X) / 2] * 10
Now, we need to find the area of the triangle. The area of a triangle is given by the formula:
Area = (base * height) / 2
Since the triangle and the trapezoid share a base, we can express the area of the triangle as:
Area of triangle = (15 * 10) / 2 = 150 / 2 = 75
It is given that the area of the trapezoid is less than twice the area of the triangle, so we can set up the following inequality:
[(15 + X) / 2] * 10 < 2 * 75
Simplifying the inequality:
(15 + X) * 10 < 150
Dividing both sides by 10:
15 + X < 15
Subtracting 15 from both sides of the inequality:
X < 0
Therefore, X is less than 0.
However, we were also given that X is less than 15 inches. So, to satisfy both conditions, the value of X lies between 0 and 15 inches.
To summarize, X is greater than or equal to 0 inches and X is less than 15 inches.