Question

what value of x will make the triangles similar by the sss similarity theorem? 15.9 59 77 96.8

Explanation:

Step1: Recall SSS Similarity Theorem

For two triangles to be similar by SSS (Side - Side - Side) similarity theorem, the ratios of their corresponding sides must be equal. That is, if we have two triangles with side lengths \(a,b,c\) and \(a',b',c'\) respectively, then \(\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}\).

In the given triangles, the first triangle has side lengths \(20\), \(20\), and \(35\). The second triangle has side lengths \(44\), \(44\), and \(x\). The sides of length \(20\) in the first triangle correspond to the sides of length \(44\) in the second triangle, and the side of length \(35\) in the first triangle corresponds to the side of length \(x\) in the second triangle.

Step2: Set up the proportion

We set up the proportion using the corresponding sides. Since \(\frac{20}{44}=\frac{35}{x}\) (because the ratio of the equal - length sides should be equal to the ratio of the third sides for SSS similarity).

To solve for \(x\), we can cross - multiply. Cross - multiplying gives us \(20\times x=35\times44\).

Step3: Solve for \(x\)

First, calculate \(35\times44\): \(35\times44 = 1540\).

Then, we have the equation \(20x = 1540\). To find \(x\), we divide both sides of the equation by \(20\): \(x=\frac{1540}{20}=77\).

Answer:

\(77\) (corresponding to the option "77")