# D ,E ,F are mid points of the sides BC ,CA and AB respectively of a triangle ABC . Find the ratio of the areas of tri.DEF and tri.ABC.

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by Razz14

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by Razz14

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The Brainliest Answer!

since,F and E are the mid points of sides BC and AC

therefore fc // bc and fc = 1/2 bc. therefore FEBD is a //gm.

then, //gm FEDB = 1/2 tri FED _________ (equation 1)

similarly, //gm. FECD = 1/2 tri. FED ________ (equation 2)

and //gm FAED. = 1/2 tri FED _______ (equation 3)

therefore, //gm FEDB = //gm FECD = //gm FAED _____ (equation 4)

now, tri. FBD + tri FED = tri FED + tri ECD = tri FED +tri FAE(from eq.4)

subtracting tri FED from the above eq.

we get,

tri FBD = ECD = FAE

now, since all the triangles are equal therefore

tri ABC = 1/4 tri FED or DEF

now taking out the ratio of the above eq.

4 * tri ABC = 1 * tri DEF (by cross multiplication)

therefore the ratio is 1:4

Ihope this helped you

pls mark brainliest