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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.

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

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