Question

ABC is a triangle D is the point on AB such that AD=1\4 AB and E is a point on AC such that AE=1\4AC if DE=2cm find BC

Answer 1

by thales theorem we got bc 8 cm

Answer 2

Answer:

The length of BC is 8 cm

Step-by-step explanation:

Given ABC is a triangle D is the point on AB such that AD=1/4 AB and E is a point on AC such that AE=1/4AC if DE=2cm

We have to find the BC

$AD=\frac{1}{4}AB$ ⇒ $\frac{AD}{AB}=\frac{1}{4}$

As the length of two corresponding sides is in the same proportion and the included angle between the sides is common then triangles are similar and the ratio of the lengths of corresponding sides is the same;

$\frac{AD}{AB} = \frac{AE}{AC} = \fac{DE}{BC}$

$\frac{1}{4}=\frac{2}{BC}$

$BC=8 cm$

The length of BC is 8 cm