Answer:
QT = 45
Step-by-step explanation:
ST = 65
SP = 26
RQ = 30
QT = 4x - 3
Given that ∆STR is similar to ∆PTQ, therefore:
[tex] \frac{ST}{PT} = \frac{RT}{QT} [/tex]
Plug in the values
[tex] \frac{65}{65 - 26} = \frac{30 + (4x - 3)}{4x - 3} [/tex]
Solve for x
[tex] \frac{65}{39} = \frac{30 + 4x - 3)}{4x - 3} [/tex]
[tex] \frac{5}{3} = \frac{27 + 4x}{4x - 3} [/tex]
Cross multiply
[tex] 5(4x - 3) = 3(27 + 4x) [/tex]
[tex] 20x - 15 = 81 + 12x [/tex]
Collect like terms
[tex] 20x - 12x = 81 + 15 [/tex]
[tex] 8x = 96 [/tex]
Divide both sides by 8
[tex] x = \frac{96}{8} [/tex]
[tex] x = 12 [/tex]
✅QT = 4x - 3
Plug in the value of x
QT = 4(12) - 3 = 48 - 3
QT = 45
