How i solve the problem of class 10th of chapter Triangles of exercise 6.4. How i solve this question in easy way Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

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# Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals. Q.7

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Given, ABCD is a square whose one diagonal is AC. Î”APC and Î”BQC are two equilateral triangles described on the diagonals AC and side BC of the square ABCD.

Area(Î”BQC) = Â½ Area(Î”APC)

Since, Î”APC and Î”BQC are both equilateral triangles, as per given,

âˆ´ Î”APC ~ Î”BQC [AAA similarity criterion]

âˆ´ area(Î”APC)/area(Î”BQC) = (AC

^{2}/BC^{2}) = AC^{2}/BC^{2}Since, Diagonal = âˆš2 side = âˆš2 BC = AC

â‡’ area(Î”APC) = 2Â Ã— area(Î”BQC)

â‡’ area(Î”BQC) = 1/2area(Î”APC)

Hence, proved.