Question

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

Answer 1

Answer:

PT = 16.3 units

Step-by-step 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.

$\frac{PQ}{PS}=\frac{PR}{PT}$

$\frac{12+28}{28}= \frac{PT+7}{PT}$

$\frac{40}{28}=1+\frac{7}{PT}$

$\frac{10}{7}-1=\frac{7}{PT}$

$\frac{10-7}{7}=\frac{7}{PT}$

PT = $\frac{49}{3}$

PT = 16.3 units