Question

Refer to the diagram below. Surveyors know that ∆PQR and ∆STR are similar. What is PQ, the distance across the lake?

3.20 km
3.60 km
2.80 km​
3.24 km

Answer 1

Answer : The distance across the lake (PQ) is, 3.24 km

Step-by-step explanation :

As we are given that ∆PQR and ∆STR are similar triangles.

By (BPT) basic proportionality theorem,

`(TR)/(QR)=(ST)/(PQ)` ............(1)

Given:

Length of TR = 1.25 km

Length of ST = 1.80 km

Length of QR = 2.25 km

Now put all the given values in the equation 1, we get:

`(1.25)/(2.25)=(1.80)/(PQ)`

`PQ=3.24`

Thus, the distance across the lake (PQ) is, 3.24 km