Question:
In order for the two triangles shown to be similar, what is one possible value for x?
In order for the two triangles shown to be similar, what is one possible value for x?
Updated On: Sep 30, 2025
- 8 in
- 10 in
- 16 in
- 20 in
- 24 in
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The Correct Option is B
Solution and Explanation
Step 1: Set up the proportion for similar triangles
The ratio of corresponding sides for similar triangles is constant. So, we have the equation:
\[ \frac{4 \text{ in.}}{7 \text{ in.}} = \frac{x}{28 \text{ in.}} \]
Convert \( 21 \frac{3}{4} \) ft. to inches:
\( 21 \frac{3}{4} \) ft. = \( 21 \frac{3}{4} \times 12 = 28 \) in.
Step 2: Solve for x
Now, solve the proportion:
\[ \frac{4}{7} = \frac{x}{28} \]
Cross multiply:
\[ 4 \times 28 = 7 \times x \implies 112 = 7x \implies x = \frac{112}{7} = 16 \text{ in.} \]
Step 3: Conclusion
Thus, one possible value for \( x \) is 16 in. Therefore, the final answer is:
16 in.
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