another math question?

the diagonal of a square is 5 square root 14 what is the area of the square

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  • ?
    Lv 7
    8 months ago

    The diagonal of a square cuts the square into 2 right triangles,

    each with with angles measuring 45°-90°-45°.

    These types of triangles carry a special ratio between sides:

    .....leg1:hypotenuse:leg2 = 1:√2:1

    So if the diagonal is 5√14, then

    ..........................5√14

    .....leg1 = leg2 = ------ = 5√7

    ...........................√2

    and the area of the square is (5√7)² = 25(7) = 175...........ANS

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  • Pope
    Lv 7
    8 months ago

    The area of a square is one-half the square of a diagonal. This simple formula is possible because the diagonals of a square are perpendicular and equal in length.

    [5√(14)]²/2 = 175

  • sepia
    Lv 7
    8 months ago

    Area of Square = ½ × d^2 

    The diagonal of a square is 5√14

    The area of the square = ((5√14)^2) / 2  = 175 

  • Anonymous
    8 months ago

    For an equilateral right triangle, the hypotenuse is the length of the side multiplied by the square root of 2. So the length of the side is:

    x(square root of 2) = 5(square root of 7)

    x = 5square root 7

    Area = x^2

    (5(square root 7))^2 = 25 * 7 = 175

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  • Anonymous
    8 months ago

    Area can be found by multiplying squaring diagonal by 10.

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