The perimeters of two similar triangles ABC and PQR are 32 cm and 24 cm respectively. If PQ = 12 cm, find AB.
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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 △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.
Step 3: Solve for AB
To find the length of side AB, we rearrange the equation. We multiply both sides by 12 cm to isolate AB.
Step 4: Calculate the Final Value of AB
First, simplify the fraction 2432 to 34. Then, multiply 34 by 12 cm to get the final length of AB.