The length of a rectangle is increased by %.By what percent would the width have to be decreased to maintain?

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The length of a rectangle is increased by %. By what percent would the width have to be decreased to maintain the same area?

# The area of a triangle inscribed in a circle having radius cm. is equal to . sq. cm. If one of the sides of the triangle is cm,. find one of the other sides?

Sol.(please)

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  • .%

  • () Area = length × width

    Area = / length × “x” width

    “x” = / = .% = width

    Example: L = , W =

    % L = , % W = .

    × . = = ×

    () Area (triangle) = ½ base × height

    Let base be cm

    Notice that × cm (radius) = cm (diameter)

    therefore one side of the triangle is a diameter of the circle.

    Area = cm × h

    . cm² /cm = height = . cm

    Since the height of the triangle is perpendicular to it’s base;

    arcsin (.cm/cm) is the angle between the center of the circle and the intersection of the height and the circumference. Cosine (arcsine./) × cm is the distance between the center of the circle and the intersection of the height and the cm side length.

    Using pythagoras’ theorem: the three sides are approximately . cm, . cm, and cm

    Sorry I can’t check this, but I don’t have inverse trig.

    Source(s): http://en.wikipedia.org/wiki/Circumscribed_circle

  • enable L = length of the unique rectangle W = width of the unique rectangle unique section = A = LW If the size of the rectangle will become a million.L and for the section to be the comparable by using fact the unique section, then LW = (a million.)(L)(W – x) the place x = proportion which the width could be decreased Simplifying the above, W = a million.(W – x) W = a million.W – a million.x a million.x = a million.W – W x = .W From the above, the width of the rectangle could through decreased through % to determine that the condition of the problem to be happy. desire this helps.

  • . A * B = X >> A * .B = X >> A * /B = X >>> CA * /CB = X because c * /c =

    .A * /.B = X reduce by /%

    . . = / b h . = b h ./ = h = . cm

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