Questions: For questions 8-9, each pair of polygons is similar. Set up a proportion and solve for the value of x. 8. QRTS~LMON

Transcript text: For questions 8-9, each pair of polygons is similar. Set up a proportion and solve for the value of $x$. 8. QRTS~LMON

Solution

Solution Steps

Step 1: Identify corresponding sides

The problem states that QRTS is similar to LMON. This means that the ratio of corresponding sides is equal. The corresponding sides are: QR and LM RS and MO ST and ON TQ and NL

Step 2: Set up a proportion

We are given QR = 15 inches, LM = 20 inches, and MO = 12 inches. We need to find the length of RS, which corresponds to MO. Let RS = x. We can set up the proportion: \$\frac{QR}{LM} = \frac{RS}{MO}\$

Step 3: Substitute the given values

Substitute the given values into the proportion: \$\frac{15}{20} = \frac{x}{12}\$

Step 4: Solve for x

Cross-multiply: $20x = 15 \times 12$ $20x = 180$ Divide both sides by 20: $x = \frac{180}{20}$ $x = 9$