In riangle ACE, BF ext is parallel to CE, and B lies on AC, F lies on AE. If BC = rac38 AC, what is the ratio racABAC?

April 14, 2026Mathematics

ScanSolve AI Answer

April 14, 2026

Answer

the ratio $\frac{AB}{AC} = \frac{5}{8}$

Step 1: Use the parallel lines $BF \parallel CE$ to establish ratios. Given $BF \parallel CE$ in $\triangle ACE$ . By the Basic Proportionality Theorem (or similar triangles $\triangle ABF \sim \triangle ACE$ ), we have: $\frac{AB}{AC} = \frac{AF}{AE} = \frac{BF}{CE}$ We are given $BC = \frac{3}{8} AC$ . Since $AB + BC = AC$ , we can write $AB = AC - BC = AC - \frac{3}{8} AC = \frac{5}{8} AC$ . Therefore, the ratio $\frac{AB}{AC} = \frac{5}{8}$ . This implies $\frac{

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

More Mathematics Questions

QFind the local time of Yanga in Tanzania, which is located at longitude 39° East, if it is 12:00 noo…QCacheprobe1780603963316: A cyclist rides 90 km in 2 hours. Average speed in km/h? Show work.QCacheprobe1780603930644: A cyclist rides 90 km in 2 hours. Average speed in km/h? Show work.QCacheprobe1780603930644: A cyclist rides 90 km in 2 hours. Average speed in km/h? Show work.QCacheprobe1780603897115: A cyclist rides 90 km in 2 hours. Average speed in km/h? Show work.

See all Mathematics questions →

Still have questions?

Quick Answer

Use the parallel lines BF CE to establish ratios. Given BF CE in ACE.

Asked on April 14, 2026Mathematics

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 AnswerAnswered on April 14, 2026

Step 1: Use the parallel lines BF CE to establish ratios. Given BF CE in ACE. By the Basic Proportionality Theorem (or similar triangles ABF ACE), we have: (AB)/(AC) = (AF)/(AE) = (BF)/(CE) We are given BC = (3)/(8) AC. Since AB + BC = AC, we can write AB = AC - BC = AC - (3)/(8) AC = (5)/(8) AC. Therefore, the ratio (AB)/(AC) = (5)/(8). This implies $