This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the given information and the relationship between the triangles. We are given that PQR is similar to PWY. We are also given the lengths of the parallel sides: |WY| = 6 cm and |QR| = 15 cm. The length of a segment on one side is given: |WP| = 4 cm. We need to find the length of |WQ|. Step 2: Use the similarity of the triangles to find the ratio of corresponding sides. Since PQR PWY, the ratio of their corresponding sides is equal. The side WY in PWY corresponds to the side QR in PQR. The side PW in PWY corresponds to the side PQ in PQR. The ratio of similarity k can be found using the lengths of WY and QR: k = (|WY|)/(|QR|) = 6 cm15 cm = (2)/(5) Step 3: Use the ratio of similarity to find the length of PQ. Now, we apply this ratio to the sides PW and PQ: (|PW|)/(|PQ|) = k Substitute the known values: 4 cm|PQ| = (2)/(5) To solve for |PQ|, cross-multiply: 2 × |PQ| = 4 cm × 5 2 × |PQ| = 20 cm |PQ| = 20 cm2 |PQ| = 10 cm Step 4: Calculate the length of WQ. From the diagram, the segment PQ is composed of two parts, PW and WQ. So, |PQ| = |PW| + |WQ|. We know |PQ| = 10 cm and |WP| = 4 cm. 10 cm = 4 cm + |WQ| Subtract 4 cm from both sides to find |WQ|: |WQ| = 10 cm - 4 cm |WQ| = 6 cm The length of WQ is 6 cm.