Question

pentagon i is a scaled copy of pentagon h.
what is the value of j?

Explanation:

Step1: Find the scale factor

Since pentagon \(I\) is a scaled copy of pentagon \(H\), we can find the scale factor by comparing the corresponding sides. Let's use the top - side of the pentagons. The length of the top - side of pentagon \(H\) is \(16\), and the length of the top - side of pentagon \(I\) is \(12\). The scale factor \(k=\frac{12}{16}=\frac{3}{4}\)

Step2: Calculate the value of \(j\)

We know that the side of length \(20\) in pentagon \(H\) corresponds to the side of length \(j\) in pentagon \(I\). Using the scale factor formula \(j = 20\times k\). Substitute \(k = \frac{3}{4}\) into the formula: \(j=20\times\frac{3}{4}\)

$$j=\frac{20\times3}{4}= 15$$

Answer:

\(15\)