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    Construct the quadrature of 3 squares. Let a = 3 be a line segment that extends along the y-axis from the origin O to the point B at (0,3). Let b = 4 be a line segment that extends along the x-axis from the origin O to the point A at (4,0). Let x be the hypotenuse of triangle ABO.

    Let c = 2 be a line segment extending above the x-axis from point A to a point C, forming a right angle at CAB. Let d be the hypotenuse from C to B. Draw a perpendicular line to the x-axis from C that is called D.

    1. Show that Triangle ABO is similar to Triangle CAD, where O is the origin.

    2. Find the coordinates of C in terms of a and b.

    3. Use the distance formula to find the distance of BC.

    © BrainMass Inc. brainmass.com December 24, 2021, 8:51 pm ad1c9bdddf
    https://brainmass.com/math/triangles/similar-triangles-finding-coordinates-320903

    SOLUTION This solution is FREE courtesy of BrainMass!

    Construct the quadrature of 3 squres. Let a = 3 be a line segment that extends along the y-axis from the origin O to the point B at (0,3). Let b = 4 be a line segment that extends along the x-axis from the origin O to the point A at (4,0). Let x be the hypotenus of Triangle ABO.

    Let c = 2 be a line segment extending above the x-axis from point A to a point C, forming a right angle at CAB. Let d be the hypotenus from C to B. Draw a perpendicular line to the x-axis from C that is called D.

    1. Show that Triangle ABO is similar to Triangle CAD, where O is the origin.
    In the triangle ABO, <O = 90 degrees and in the triangle CAD, <D = 90 degrees
    In the triangle ABO, < A = 45 degrees and <B = 45 degrees and in the triangle CAD, <A=45 degrees and <C = 45 degrees.
    Here the corresponding angles are same.
    Since the angles are in same measure, the two triangles ABO and CAD are similar.
    Hence, we proved.

    2. Find the coordinates of C in terms of a and b.
    C = (a/2, b + 1.5)

    3. Use the distance formula to find the distance of BC.
    First, let's find the value of x.
    X = sqrt(4^2 + 3^2)
    X = sqrt(16 + 9)
    X = sqrt(25)
    X = 5
    So the side AB = 5
    Now consider the triangle BAC, in the triangle AB = 5 and AC = 2
    BC = sqrt( AB^2 + AC^2) [By Pythagorean theorem]
    BC = sqrt(5^2 + 2^2)
    BC = sqrt(25 + 4)
    BC = sqrt(29)
    BC = 5.39

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 8:51 pm ad1c9bdddf>
    https://brainmass.com/math/triangles/similar-triangles-finding-coordinates-320903

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