Question

4 - 41.
the two polygons at right are similar. homework help

a. determine the value of x. show all work.

b. calculate the area of each polygon.

4 - 42. for each part below, decide if the triangles are similar. if they are similar, use the properties of similarity to solve for x. if they are not similar, explain why not. homework help

Explanation:

Step1: Find the scale factor

Since the two polygons are similar, the ratio of their corresponding sides is equal. We can use the vertical sides \(12\) and \(30\). The scale factor \(k=\frac{30}{12}=\frac{5}{2}\)

Step2: Set up the proportion for \(x\)

The horizontal side of the first polygon (excluding the \(6\) part) is \(10 - 6=4\). Let's use the corresponding horizontal sides. The horizontal side of the second polygon (excluding the \(15\) part) corresponds.
We know that \(\frac{x - 15}{4}=\frac{5}{2}\)

Cross - multiply: \(2(x - 15)=4\times5\)

Step3: Solve the equation

Expand: \(2x-30 = 20\)

Add \(30\) to both sides: \(2x=20 + 30\)

\(2x=50\)

Divide both sides by \(2\): \(x = 25\)

Answer:

\(x = 25\)