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.
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Another one scoddyevarau87@gmail.com — let's solve it. Problem 22: Given that ABC DEF, the ratio of their corresponding sides is equal. Step 1: Identify corresponding sides and set up the proportion. The corresponding sides are AB and DE, and AC and DF. (AB)/(DE) = (AC)/(DF) Step 2: Substitute the given values. We have AB = 8 cm, AC = 6 cm, and DF = 12 cm. 8 cmDE = 6 cm12 cm Step 3: Solve for DE. Simplify the right side: (8)/(DE) = (1)/(2) Cross-multiply: 8 × 2 = DE × 1 16 = DE Therefore, the length of side DE is: DE = 16 cm Problem 2: Given that the ratio of corresponding sides of two similar triangles is 3:5. One side of the smaller triangle is 9 cm. Step 1: Set up the ratio of the sides. Let s_S be the side of the smaller triangle and s_L be the corresponding side of the larger triangle. (s_S)/(s_L) = (3)/(5) Step 2: Substitute the given value for the side of the smaller triangle. We are given s_S = 9 cm. 9 cms_L = (3)/(5) Step 3: Solve for s_L. Cross-multiply: 9 × 5 = 3 × s_L 45 = 3 s_L Divide by 3: s_L = (45)/(3) s_L = 15 cm The corresponding side of the larger triangle is: s_L = 15 cm Send me the next one 📸