In ΔPQR, ∠Q = 90 degrees and QX is perpendicular to PR. If PQ = 15 cm and PR = 25 cm, then what is the ratio of PX : XR ?
Answer & explanation
Correct answer: option 4
Using the principle of similar triangles, since Δ PQR ~ Δ PQX, we have:
\(\frac{ PX }{ PQ }\) = \(\frac{ PQ }{ PR }\)
\(\frac{ PX }{ 15 }\) = \(\frac{ 15 }{ 25 }\)
Solving this, we get PX = 9 cm.
XR = PR - PX
= 25 - 9 = 16
Now, PX : XR = 9:16