Question

A line is parallel to BC cuts AB and AC at D and E such that AD:DB=1:2 find the ratio of areas of trapeziumBDEC and ADE so formed​

Answer 1

Answer:

and = 1/8

Step-by-step explanation:

SINCE AD:DB= 1:2

so, ar. ADE: ABC= 1/9

AR. trapezium = AR. ABC - ADE

= 9-1 =8

AR TRAPEZIUM : AR ADE =

8:1

Answer 2

Answer:

8:1

Step-by-step explanation:

As, DE || BC,

so angle ADE= angle ABC (corresponding angles)

Also, angle AED = angle ACB (corresponding angles)

so, triangle AED is similar to triangle ACB (by A-A property)

AD^2:AB^2 = area of triangle AED : area of triangle ABC

                    =1:9

area of trapezium=area of abc-area of aed

                             =8 units

so, arae of trapezium BDEC: area of triangle ADE=8:1