Question

If triangle STR ~ triangle PTQ, find QT

Answer 1

QT = 45

Explanation:

ST = 65

SP = 26

RQ = 30

QT = 4x - 3

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

`(ST)/(PT) = (RT)/(QT)`

Plug in the values

`(65)/(65 - 26) = (30 + (4x - 3))/(4x - 3)`

Solve for x

`(65)/(39) = (30 + 4x - 3))/(4x - 3)`

`(5)/(3) = (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 = (96)/(8)`

`x = 12`

✅QT = 4x - 3

Plug in the value of x

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

QT = 45