The area of triangleABCabove is at least48but no more than60. Ifyis an integer, what is one possible value ofx?
Question
The area of triangle ABC above is at least 48 but no more than 60. If y
is an integer, what is one possible value of x
?
Solution
To solve the problem regarding the area of triangle ABC, let's break this down:
1. ### Break Down the Problem
We know the area of triangle ABC is bounded by: To find possible values of , we might need an expression for the area of a triangle based on its dimensions, typically represented as:
2. ### Relevant Concepts
The area formula will depend on the dimensions given in the context. Assuming and represent the base and height respectively, we can express the area as:
3. ### Analysis and Detail
Now, we will set up the inequalities based on the area bounds: Multiplying all parts of the inequality by 2 to eliminate the fraction gives us:
4. ### Verify and Summarize
To find integer values of and , we can choose as one possible height. Now, substituting into the inequalities gives:
Dividing the entire inequality by 10 results in: As is an integer, it can take the values or .
Final Answer
One possible value of is .
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