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Question
A trapezium with 3 equal sides and one side double the equal side can be divided into ______ equilateral triangles of ______ area.
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Solution
A trapezium with 3 equal sides and one side double the equal side can be divided into 3 equilateral triangles of equal area.
Explanation:
Let ABCD be a trapezium, in which
AD = DC = BC = a ...(say)
And AB = 2a ...[Given]
Draw medians through the vertices D and C on the side AB.
∴ AE = EB = a
Now, in parallelogram ADCE, we have
AD = EC = a and AE = CD = a ...[Opposite side in a parallelogram are equal]
In ΔADE and ΔDEC,
AD = EC
AE = CD
And DE = DE ...[Common]
BY SSS, ΔADE = ΔDEC
By triangle rule, ΔADE ≅ ΔDEC
Thus, ΔADE and ΔDEC are equilateral triangles having equal sides.
Similarly, in parallelogram DEBC, we can show that ΔDEC ≅ ΔECB.
Hence, the trapezium can be divided into 3 equilateral triangles of equal area.
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