Question

solve for x. the polygon in each pair are similar.

Explanation:

Identify corresponding sides

The problem states that the polygons are similar.
We identify the corresponding sides of the two similar quadrilaterals:

• The left side of length \(12\) corresponds to the left side of length \(30\).
• The bottom side of length \(10\) corresponds to the bottom side of length \(2x + 3\).

Set up the proportion

Since the polygons are similar, the ratio of their corresponding sides must be equal:

$$ \frac{12}{30} = \frac{10}{2x + 3} $$

Simplify the ratio

Simplify the fraction on the left side:

$$ \frac{12}{30} = \frac{2}{5} $$

So the equation becomes:

$$ \frac{2}{5} = \frac{10}{2x + 3} $$

Solve for x

Cross-multiply to solve the equation:

$$ 2(2x + 3) = 5 \times 10 $$

$$ 4x + 6 = 50 $$

$$ 4x = 44 $$

$$ x = 11 $$

Answer:

• 9
• 11 (Correct answer)
• 6
• 5