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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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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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  1. Ncert solutions class 10 chapter 6-37Given, ABCD is a square whose one diagonal is AC. ΔAPC and ΔBQC are two equilateral triangles described on the diagonals AC and side BC of the square ABCD.

    Area(ΔBQC) = ½ Area(ΔAPC)

    Since, ΔAPC and ΔBQC are both equilateral triangles, as per given,

    ∴ ΔAPC ~ ΔBQC [AAA similarity criterion]

    ∴ area(ΔAPC)/area(ΔBQC) = (AC2/BC2) = AC2/BC2

    Since, Diagonal = √2 side = √2 BC = AC

    Ncert solutions class 10 chapter 6-38

    ⇒ area(ΔAPC) = 2 × area(ΔBQC)

    ⇒ area(ΔBQC) = 1/2area(ΔAPC)

    Hence, proved.

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