Question

9. In a ∆ABC DE||BC,D on AB and E on AC. If AD/DB=3/4,find BC/DE​

Answer 1

Given: DE||BC, D on AB and E on AC, AD/DB=3/4

To find: BC/DE

Solution:

• In this question first we need to prove that the two triangles are similar, so that the sides are in the same ratio.

• So now, lets consider the triangle ADE and the triangle ABC, we have:

             ang A = ang A ...........(common angle)

             ang ADE = ang ABC ............(corresponding angles)

             ang AED = ang ACB .............(corresponding angles)

• Therefore:

             triangle ADE is similar to triangle ABC  .........by AAA test.

• So, AB/AD = BC/DE

               AD/DB = 3/4

              DB/AD = 4/3

              (DB + AD) / AD = ( 4 + 3 ) / 2

              AB/AD = 7/2

• Now, we have proved that AB/AD = BC/DE

• So,

              BC/DE = 5/2

Answer:

                 So,  BC/DE = 5/2

Answer 2

The value of BC/DE​ is 7/3

Step-by-step explanation:

From the ∆ABC, we can understand that,

∠A = ∠A

∠ADE = ∠ABC

∠AED = ∠ACB

Thus, here AAA criterion is used, in this theorem, triangles are similar if the measure of all three interior angles in one triangle are the same as the corresponding angles in another.

From diagram,

AB/AD = BC/DE

From question, AD/DB = 3/4

AB/AD = (AD + DB)/AD = (3 + 4)/3

AB/AD = 7/3 = BC/DE

∴ BC/DE = 7/3