Question

in the following figures, find the measure of the side
a.
b

(\triangle abcsim\triangle ade)

a. (x=square) (type an integer or a simplified fraction.)

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle ADE\), the ratios of corresponding sides are equal. That is \(\frac{AB}{AD}=\frac{AC}{AE}\).
We know that \(AB = 2\), \(AD=AB + BD=2 + 2=4\), \(AC=x\), and \(AE=AC + CE=x + 6\).
So, \(\frac{2}{4}=\frac{x}{x + 6}\).

Step2: Cross - multiply

Cross - multiplying the equation \(\frac{2}{4}=\frac{x}{x + 6}\) gives \(2(x + 6)=4x\).
Expanding the left - hand side: \(2x+12 = 4x\).

Step3: Solve for \(x\)

Subtract \(2x\) from both sides: \(12=4x - 2x\).
So, \(2x = 12\), and \(x = 6\).

Answer:

\(6\)