Question

le similarity: sss and sas
what value of x will make the triangles similar by the sss similarity theorem?
50
x
x
75
45
45
67.5
1.5
30
20

Explanation:

Step1: Recall SSS Similarity Theorem

The SSS (Side - Side - Side) similarity theorem states that if the corresponding sides of two triangles are in proportion, then the triangles are similar. So, we need to set up a proportion between the sides of the two triangles.

Let's denote the first triangle with sides \(50\), \(x\), \(x\) and the second triangle with sides \(75\), \(45\), \(45\). For the triangles to be similar by SSS, the ratios of corresponding sides should be equal. So, we can set up the proportion \(\frac{50}{75}=\frac{x}{45}\) (we match the side of length \(50\) in the first triangle with the side of length \(75\) in the second triangle, and the side of length \(x\) in the first triangle with the side of length \(45\) in the second triangle).

Step2: Solve the Proportion

We have the proportion \(\frac{50}{75}=\frac{x}{45}\). Cross - multiply to get \(75x = 50\times45\).

First, calculate \(50\times45=2250\). Then, solve for \(x\) by dividing both sides of the equation \(75x = 2250\) by \(75\). So, \(x=\frac{2250}{75}\).

Simplify \(\frac{2250}{75}\): \(2250\div75 = 30\).

Answer:

\(30\)