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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

Refer to the diagram below Surveyors know that PQR and STR are similar What is PQ the distance across the lake320 km360 km280 km324 km class=

Respuesta :

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,

[tex]\frac{TR}{QR}=\frac{ST}{PQ}[/tex]     ............(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:

[tex]\frac{1.25}{2.25}=\frac{1.80}{PQ}[/tex]

[tex]PQ=3.24[/tex]

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

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