Question

In order for the two triangles shown to be similar, what is one possible value for x?

• A. 8 in
• B. 10 in
• C. 16 in
• D. 20 in
• E. 24 in

Answer 1

The Correct Option is B

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.