Question

If triangle STR ~ triangle PTQ, find QT

Answer 1

Answer:

QT = 45

Step-by-step explanation:

ST = 65

SP = 26

RQ = 30

QT = 4x - 3

Given that ∆STR is similar to ∆PTQ, therefore:

$\frac{ST}{PT} = \frac{RT}{QT}$

Plug in the values

$\frac{65}{65 - 26} = \frac{30 + (4x - 3)}{4x - 3}$

Solve for x

$\frac{65}{39} = \frac{30 + 4x - 3)}{4x - 3}$

$\frac{5}{3} = \frac{27 + 4x}{4x - 3}$

Cross multiply

$5(4x - 3) = 3(27 + 4x)$

$20x - 15 = 81 + 12x$

Collect like terms

$20x - 12x = 81 + 15$

$8x = 96$

Divide both sides by 8

$x = \frac{96}{8}$

$x = 12$

✅QT = 4x - 3

Plug in the value of x

QT = 4(12) - 3 = 48 - 3

QT = 45