Answer:
ST = 16
Step-by-step explanation:
The similar triangles are given as triangle PQR similar to triangle STU.
That makes sides PQ and ST corresponding sides. It also makes sides PR and SU corresponding sides. The ratios of the lengths of corresponding sides of similar triangles are equal.
[tex] \dfrac{ST}{PQ} = \dfrac{SU}{PR} [/tex]
[tex] \dfrac{5x + 1}{36} = \dfrac{11x - 5}{63} [/tex]
Multiply both sides by 9.
[tex] \dfrac{5x + 1}{4} = \dfrac{11x - 5}{7} [/tex]
Cross multiply.
[tex] 7(5x + 1) = 4(11x - 5) [/tex]
Distribute on both sides.
35x + 7 = 44x - 20
Subtract 44x from both sides.
-9x + 7 = -20
Subtract 7 from both sides.
-9x = -27
Divide both sides by -9.
x = 3
ST = 5x + 1 = 5(3) + 1 = 15 + 1 = 16
Answer: ST = 16
