We are given the perimeter of ABC as 32 cm, the perimeter of PQR as 24 cm, and the side PQ as 12 cm. We substitute these values into the ratio derived in the previous step.

First, simplify the fraction (32)/(24) to (4)/(3). Then, multiply (4)/(3) by 12 cm to get the final length of AB.

The perimeters of two similar triangles ABC and PQR are 32 cm and 24 cm respectively. If PQ = 12 cm, find AB.

Answer: $AB = 16 \text{ cm}$

Step-by-step solution

Step 1: Understand the Property of Similar Triangles

For similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides. This is a fundamental property that allows us to relate the given perimeters to the unknown side length.

Step 2: Substitute Given Values into the Ratio

We are given the perimeter of $\triangle ABC$ as $32 \text{ cm}$ , the perimeter of $\triangle PQR$ as $24 \text{ cm}$ , and the side $PQ$ as $12 \text{ cm}$ . We substitute these values into the ratio derived in the previous step.

Step 3: Solve for AB

To find the length of side $AB$ , we rearrange the equation. We multiply both sides by $12 \text{ cm}$ to isolate $AB$ .

Step 4: Calculate the Final Value of AB

First, simplify the fraction $\frac{32}{24}$ to $\frac{4}{3}$ . Then, multiply $\frac{4}{3}$ by $12 \text{ cm}$ to get the final length of $AB$ .

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