Question

the area of two similar triangle is 144cm and 49cm.if the median of greater side of two triangle is 6cm, find the coreesponding of median other triangle

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Let the triangles be ΔABC and ΔDEF,

Given- AX=6cm, ar(ABC)=144cm and ar(DEF)=49cm

To find -  DY

In  ΔABC and ΔDEF,

AB/DE = BC/EF = AC/DF         - 1

∠ABC = ∠DEF   - 2     (correspaonding parts of similer triangles)

ar(ABC)/ar(DEF) = AB²/DE² = BC²/EF² = AC²/DF²   -3  (area ratio theoram)

In ΔABX and ΔDEY,

AB/DE = BC/EF (from 1)

AB/DE = 2BX/2EY   (X and Y are midpoints)

AB/DE = BX/EY

∠ABC = ∠DEF  (from 2)

∴ ΔABX is similer to ΔDEY   (SAS rule)

AB/DE = AX/DY

Squaring both sides

AB²/DE² = AX²/DY²

ar(ABC)/ar(DEF) = AB²/DE² = AX²/DY²   (from 3)

ar(ABC)/ar(DEF) = AX²/DY²

144/49 = AX²/DY²

12/7 = AX/DY

12/7 = 6/DY

DY = 3.5 cm