Question

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

Answer 1

Incomplete Question the Complete Question is here

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:

The Last option is correct 3.24 km

Therefore the distance across the lake is PQ = 3.24 km.

Step-by-step explanation:

Given:

ΔPQR and ΔSTR are Similar

ST = 1.80 km

TR = 1.25 km

QR = 2.25 km

To Find:

Distance across the lake, PQ = ?

Solution:

ΔPQR ~ ΔSTR ..........Given:

If two triangles are similar then their sides are in proportion.  

$\dfrac{PQ}{ST} =\dfrac{QR}{TR} \textrm{corresponding sides of similar triangles are in proportion}$

Substituting the values we get

$\dfrac{PQ}{1.80} =\dfrac{2.25}{1.25}\\\\PQ=\dfrac{4.05}{1.25}=3.24\ km\\\therefore PQ = 3.24\ km$

 Therefore the distance across the lake is PQ = 3.24 km.