Question

tuvwx ~ ijkgh. find jk and ij.
jk=
ij=

Explanation:

Step1: Find the scale factor

Since \(TUVWX\sim IJKGH\), the scale factor \(k\) can be found by comparing corresponding sides. Let's use \(WX = 6\) and \(HI=4\). The scale factor \(k=\frac{HI}{WX}=\frac{4}{6}=\frac{2}{3}\).

Step2: Find \(JK\)

Corresponding side to \(JK\) is \(VW\). \(VW = 8\). Using the proportion \(\frac{JK}{VW}=k\), so \(JK=\frac{2}{3}\times8=\frac{16}{3}\) (This is wrong, we should use \(TX = 8\) and \(JI = 4\) to get scale factor. Correct scale factor \(k=\frac{HI}{TX}=\frac{4}{8}=\frac{1}{2}\). Then for \(JK\) (corresponds to \(VX\)), \(VX = 10\), \(JK=\frac{1}{2}\times10 = 5\))

Step3: Find \(IJ\)

Corresponding side to \(IJ\) is \(UT\). \(UT = 6\). Using the proportion \(\frac{IJ}{UT}=k\), since \(k = \frac{1}{2}\), then \(IJ=\frac{1}{2}\times6=3\)

Answer:

\(JK = 5\), \(IJ=3\)