Question

In triangle ABC, if DE || BC and DE : BC = 5 : 8, then find the ratio of areas of trapezium BCED and triangle ABC

Answer 1

Answer:

Step-by-step explanation:

IN tri ADE and tri ABC

DE//BC

so,

angle A = angle A [common angle]

angle ADE = angle ABC [corresponding angles]

so tri ADE ~ tri ABC by A.A test

area of tri ABC - area of tri DEF/area of tri ABC = DE^2/BC^2

[area of tri ABC - area of tri DEF = area of trapezium BCED]

area of trapezium BCED = 5^2/8^2 = 25/81

by the theorem ,

ratio of areas of two triangle is equal to square of the corresponding sides

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