Step-by-step explanation:
[tex] \frac{6x - 2}{30} = \frac{5x + 13}{36} \\ 36(6x - 2) = 30(5x + 13) \\ 6(6x - 2) = 5(5x + 13) \\ 36x - 12 = 25x + 65 \\ (36 - 25)x = (65 + 12) \\ 11x = 77 \\ x = \frac{77}{11} \\ x = 7[/tex]
You can use the properties that similar triangles have sides scaled.
The value of x is 7.
Since it is given that PTS ~ PQR, thus, let the scaling is done by factor f. Then we have:
[tex]|PT| = f \times |PQ|\\ |TS| = f \times |QR|\\ |SP| = f \times |RP|[/tex]
Thus, we get the ratio of length of PT and length of TS as:
[tex]\dfrac{|PT|}{|TS|} = \dfrac{f \times |PQ|}{f \times |QR|} = \dfrac{|PQ|}{|QR|}[/tex]
Using the values specified in the given figure for above obtained equation, we get:
[tex]\dfrac{|PT|}{|TS|} = \dfrac{|PQ|}{|QR|}\\
\\
\dfrac{36}{30} = \dfrac{5x + 13}{6x-2}\\
\\
\text{Cross multiplying, the denominators},\\\\
36(6x-2) = 30(5x+13)\\
216x - 72 = 150x + 390\\
216x - 150x = 390 + 72\\
66x = 462\\\\
x = \dfrac{462}{66}\\\\
x = 7[/tex]
Thus, the obtained value of x is 7.
Learn more about similar triangles here:
https://brainly.com/question/19387334
