Question

consider the figure below showing three similar triangles. which statement about this figure is true? 4 of 11 questions since all three triangles are similar, you can use a proportion to solve for \\( \overline{bd} \\) and then use the pythagorean theorem to solve for \\( x \\) in this equation: \\( 20^{2}+(\overline{bd})^{2}=x^{2} \\). since all three triangles are similar, you can use a proportion to solve for \\( \overline{bd} \\) and then use the pythagorean theorem to solve for \\( x \\) in this equation: \\( 16^{2}+(\overline{bd})^{2}=x^{2} \\). since all three triangles are similar, you can use a proportion to solve for \\( \overline{bd} \\) and then use the pythagorean theorem to solve for \\( x \\) in this equation: \\( 4^{2}+(\overline{bd})^{2}=x^{2} \\). since all three triangles are similar, you can use a proportion to solve for \\( \overline{bd} \\) and then use the pythagorean theorem to solve for \\( x \\) in this equation: \\( 24^{2}+(\overline{bd})^{2}=x^{2} \\).

Explanation:

Step1: Find the length of \(AD\)

Since \(AC = 20\) and \(DC=4\), then \(AD=AC - DC\). So \(AD = 20 - 4=16\).

Step2: Analyze the Pythagorean - theorem application for side \(x\)

In right - triangle \(ABD\), by the Pythagorean theorem \(x^{2}=AD^{2}+BD^{2}\). Substituting \(AD = 16\) into the formula, we get \(x^{2}=16^{2}+BD^{2}\).

Answer:

Since all three triangles are similar, you can use a proportion to solve for \(\overline{BD}\) and then use the Pythagorean theorem to solve for \(x\) in this equation: \(16^{2}+(\overline{BD})^{2}=x^{2}\).