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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?

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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: 48Area60 48 \leq \text{Area} \leq 60 To find possible values of x x , we might need an expression for the area of a triangle based on its dimensions, typically represented as: Area=12×base×height \text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

2. ### Relevant Concepts

The area formula will depend on the dimensions given in the context. Assuming x x and y y represent the base and height respectively, we can express the area as: Area=12×x×y \text{Area} = \frac{1}{2} \times x \times y

3. ### Analysis and Detail

Now, we will set up the inequalities based on the area bounds: 4812×x×y60 48 \leq \frac{1}{2} \times x \times y \leq 60 Multiplying all parts of the inequality by 2 to eliminate the fraction gives us: 96x×y120 96 \leq x \times y \leq 120

4. ### Verify and Summarize

To find integer values of x x and y y , we can choose y=10 y = 10 as one possible height. Now, substituting y y into the inequalities gives:

96x×10120 96 \leq x \times 10 \leq 120 Dividing the entire inequality by 10 results in: 9.6x12 9.6 \leq x \leq 12 As x x is an integer, it can take the values 10,11, 10, 11, or 12 12 .

Final Answer

One possible value of x x is 10 10 .

This problem has been solved

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