Question

d e f are respectively the midpoints of sides ab BC and CA of triangle ABC find the ratio of the areas of triangle d e f and triangle ABC ​

Answer 1

Answer:

Step-by-step explanation:

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DEF are respectively the midpoints of sides AB, BC and CA of triangle ABC, then: Ratio of area of triangle DEF :  area of triangle ABC = 1 : 4

Solution:

In the given question, we know Triangle DEF formed with midpoints is similar to the Outer Triangle ABC

On the basis of the similarity, we can say,

If two triangles are similar then the ratio of their area is equal to the square of the ratio of their corresponding sides

Mathematically can be written as :-

Since, DECF is a parallelogram. So DE = FC

On substituting:

Also, F is the midpoint of AC

Hence ratio of area of triangle DEF and triangle ABC is given as:

Ratio of area of triangle DEF :  area of triangle ABC = 1 : 4