Understanding the Triangle and Proportions
Given triangle ABC with DE parallel to CB, we can utilize the properties of similar triangles. Since DE is parallel to CB, triangles ADE and ABC are similar.
Known Measurements
- AB = 4 cm
- AD = 14 cm
- DE = 12 cm
- BC = 15 cm
Using the Properties of Similar Triangles
From the similarity of triangles ADE and ABC, we can set up the following proportion:
- (AD / AB) = (DE / BC)
Substituting the known values:
- (14 / 4) = (12 / 15)
Simplifying the Proportion
Cross-multiplying gives:
- 14 * 15 = 4 * 12
This simplifies to:
- 210 = 48 (which confirms the proportion is correct)
Finding AC
To find AC, we can use the ratio of the sides derived from the similarity:
- Since AD/AB = AC/AB (AC is the remaining side of the triangle similar to AB)
Using the values:
- AC = (AB * AD) / AB = (4 * 14) / 4 = 14 cm
Finding AE
To solve for AE, we can use the proportion of DE to BC:
- AE = (DE / BC) * AB = (12 / 15) * 4
Calculating this gives:
- AE = (12 * 4) / 15 = 48 / 15 = 3.2 cm
Final Results
- AC = 14 cm
- AE = 3.2 cm
This method helps in determining the lengths of sides AC and AE using properties of similar triangles and proportionality.