Sum of the areas of two squares is 468 m square if the difference of their perimeter is 24 m find the sides of the two square .​

Sum of the areas of two squares is 468 m square if the difference of their perimeter is 24 m find the sides of the two square .​

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2 thoughts on “Sum of the areas of two squares is 468 m square if the difference of their perimeter is 24 m find the sides of the two square .​”

  1. The Olympic motto “Citius, Altius, Fortius” (“Faster, Higher, Stronger”) was coined by Father Henri Didon, who was a close friend of Baron Pierre de Coubertin. It was adopted by the IOC in 1894.

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  2. Answer:

    Let the sides of the first and second square be X and Y .

    Area of the first square = (X)²

    Area of the second square = (Y)²

    According to question,

    (X)² + (Y)² = 468 m² ——(1).

    Perimeter of first square = 4 × X and Perimeter of second square = 4 × Y

    According to question,

    4X – 4Y = 24 ——–(2)

    From equation (2) we get,

    4X – 4Y = 244X–4Y=24

    4(X-Y) = 244(X−Y)=24

    X – Y = 24/4X–Y=24/4

    X – Y = 6X–Y=6

    X=6+Y———(3)

    Putting the value of X in equation (1)

    (X)² + (Y)² = 468(X)²+(Y)²=468

    = > (6+Y)² + (Y)² = 468

    = > (6)² + (Y)² + 2 × 6 × Y + (Y)² = 468

    = > 36 + Y² + 12Y + Y² = 468

    = > 2( Y² + 6Y – 216) = 0

    = > Y² + 6Y – 216 = 0

    = > Y² + 18Y – 12Y -216 = 0

    = > Y(Y+18) – 12(Y+18) = 0

    = > (Y+18) (Y-12) = 0

    Putting Y = 12 in EQUATION (3)

    X = 6+Y = 6+12 = 18X=6+Y=6+12=18

    Side of first square = X = 18 m

    Side of second square = Y = 12 m.

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