The value of QT in the figure is 45
How to determine proportional sides in similar triangles
From the figure
Given that ∆STR is similar to ∆PTQ,
For similar triangles their corresponding sides are proportional.
Therefore,
PT/ST = QT/RT
PT = ST - SP
= 65 - 26 = 39
QT = 4x -3, RT = 4x - 3 + 30
RT = 4x + 27
Let's find x
39/65 = 4x - 3/4x + 27
39(4x + 27) = 65(4x - 3)
Expand and simplify both sides of the equation:
156x + 1053 = 260x - 195
1053 + 195 = 260x - 156x
Combine like terms:
1248 = 104x
x = 1248/104
Simplify the fraction:
x = 12
Therefore, the solution to the equation is x = 12
QT = 4x - 3
= 4(12) -3
= 48 - 3 = 45
The value of QT is 45