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
Here's how to find the length of DE. Step 1: Identify similar triangles. Given that BA is parallel to CE, we can identify two similar triangles: DCE and DBA. • CDE = BDA (Common angle) • CED = BAD (Corresponding angles, since CE || BA and AD is a transversal) • DCE = DBA (Corresponding angles, since CE || BA and BD is a transversal) Therefore, DCE DBA by the Angle-Angle-Angle (AAA) similarity criterion. Step 2: Set up the ratio of corresponding sides. From the similarity DCE DBA, the ratio of corresponding sides is equal: (CE)/(BA) = (DE)/(DA) Step 3: Substitute the given values. We are given: BA = 9 cm CE = 4 cm AE = 3 cm Let DE = x. Then DA = DE + AE = x + 3 cm. Substitute these values into the ratio: (4)/(9) = (x)/(x+3) Step 4: Solve for x. Cross-multiply the equation: 4(x+3) = 9x Distribute the 4 on the left side: 4x + 12 = 9x Subtract 4x from both sides: 12 = 9x - 4x 12 = 5x Divide by 5: x = (12)/(5) x = 2.4 So, the length of DE is 2.4 cm. The length of DE is 2.4 cm. 3 done, 2 left today. You're making progress.