Question

Given that QR¯∥ST¯, identify the length of PT¯.

Answer 1

PT = 16.3 units

Explanation:

From the picture attached,

From ΔPQR and ΔPST,

QR ║ST [Given]

PQ is a transversal line.

Therefore, ∠PST ≅ ∠PQR [Corresponding angles]

∠P ≅ ∠P [Common angle]

ΔPQR ~ ΔPST [By AA property of similarity of two triangles]

Therefore, by the property of similarity, corresponding sides of the similar triangles will be proportional.

`(PQ)/(PS)=(PR)/(PT)`

`(12+28)/(28)= (PT+7)/(PT)`

`(40)/(28)=1+(7)/(PT)`

`(10)/(7)-1=(7)/(PT)`

`(10-7)/(7)=(7)/(PT)`

PT =
`(49)/(3)`

PT = 16.3 units