The value of Side DC is 4.
What are similar triangles?
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
We have three similar triangles because each has a right angle and shares an angle. Let's write the angles in order: opposite to the short leg, long leg, and the hypotenuse.
CAB ≡ BAD ≡ CBD
Or as ratios,
CA:AB:CB = BA:AD:BD = CB:BD:CD
We also know
AC = AD + CD
(AD+CD):AB:CB = BA:AD:BD = CB:BD:CD
(AD+CD)/CB=CB/CD
Let CD = x
(5 +x )/6 = 6/x
(5+x)*x = 6*6
5x + x² = 36
x² + 5x - 36 = 0
x² + 9x -4x -36 = 0
x(x+9 ) -4 (x +9 ) = 0
(x-4)(x+9) = 0
x= 4, -9
We reject the negative root and conclude x=4
Therefore, Side DC is 4.
To know more about similar triangles refer to :
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