High School

We appreciate your visit to In triangle ABC point P in AC such that AP PC 3 2 If the area of triangle BPC 14 text m 2 find the. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

In \(\triangle ABC\), point \(P \in AC\) such that \(AP:PC = 3:2\). If the area of \(\triangle BPC = 14 \text{ m}^2\), find the area of \(\triangle ABP\) and the area of \(\triangle ABC\).

Answer :

Final answer:

The area of triangle ABP is 21 m² and the area of triangle ABC is 35 m², computed using the ratios provided and the given area of triangle BPC.

Explanation:

The ratio of AP to PC is given as 3:2, meaning that line AC is divided into 5 equal parts where AP is 3 parts and PC is 2 parts. The areas of triangles ABP and BPC are proportional to the lengths of line segments AP and PC respectively. As the area of triangle BPC is given as 14 m², we can divide this by 2 (the number of parts that make up line segment PC) to find the area of one part, which is 7 m². Thus, the area of triangle ABP is 7 m² * 3 (the number of parts that make up line segment AP), which equals 21 m². Add together the areas of the two triangles ABP and BPC (21 m² + 14 m²) to find the area of whole triangle ABC, which equals 35 m².

Learn more about Area of Triangle here:

https://brainly.com/question/27683633

#SPJ11

Thanks for taking the time to read In triangle ABC point P in AC such that AP PC 3 2 If the area of triangle BPC 14 text m 2 find the. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada