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When triangle ABC is similar to triangle PQR, with A, B, and C corresponding to P, Q, and R, respectively, it is customary to write ABC ∼ PQR. Suppose that AB = 4, BC = 5, CA = 6, and RP = 9. Find PQ and QR.

Respuesta :

Answer:

PQ = 6 and QR = 7.5

Step-by-step explanation:

The lengths of the sides of two similar triangles are proportional. That is, if Δ ABC is similar to Δ PQR, then the following equation is established.

[tex]\frac{AC}{PR}=\frac{AB}{PQ}=\frac{BC}{QR}[/tex]

[tex]\frac{6}{9} = \frac{4}{PQ} = \frac{5}{QR}[/tex]

[tex]\frac{6}{9} = \frac{4}{PQ}[/tex]

PQ = 6

[tex]\frac{6}{9} = \frac{5}{QR}[/tex]

QR = 7.5