Question

In ∆ABC, DE || BC If DB = 1.4 cm, AD = 3.5 cm EC = 2.5 cm then find AE.

Answer 1

Answer:

The length of AE is 6.25 cm.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

We have given that,

$\sf\:In\:\triangle\:ABC\\\\\\\bullet\sf\:DE\:\parallel\:BC\\\\\\\bullet\sf\:DB\:=\:1.4\:cm\\\\\\\bullet\sf\:AD\:=\:3.5\:cm\\\\\\\bullet\sf\:EC\:=\:2.5\:cm$

We have to find AE.

We know that,

$\sf\:In\triangle\:ABC\:,\:DE\:\parallel\:BC\\\\\\\therefore\pink{\sf\:\dfrac{AD}{DB}\:=\:\dfrac{AE}{EC}}\sf\:\:\:-\:-\:[\:Basic\:Proportionality\:Theorem\:]\\\\\\\implies\sf\:\dfrac{3.5}{1.4}\:=\:\dfrac{AE}{2.5}\\\\\\\implies\sf\:3.5\:\times\:205\:=\:AE\:\times\:1.4\\\\\\\implies\sf\:AE\:=\:\dfrac{\cancel{3.5}\:\times\:2.5}{\cancel{1.4}}\\\\\\\implies\sf\:AE\:=\:\dfrac{0.5\:\times\:2.5}{0.2}\\\\\\\implies\sf\:AE\:=\:\cancel{\dfrac{1.25}{0.2}}\\\\\\\implies\boxed{\red{\sf\:AE\:=\:6.25\:cm\:}}$

Additional Information:

Basic Proportionality Theorem:

1. This is a theorem related to triangles with a parallel side drawn to one of the three sides of the triangle.

2. This thereom states that,

If in a triangle, a line is drawn parallel to a side of the triangle, then the intercepts made by two transversals and the parallel line are in the same proportion.

3. This theorem is also known as B.P.T. in a short form.