In the diagram below, QR is parallel to NO. If the length of NO is the same as the length of QP, NP=21, and QR=10, find the length of QP. Figures are not necessarily drawn to scale. State your answer in the simplest radical form, if necessary.
Answer :
The length of [tex]\(QP\)[/tex] is 21.
Since NO is parallel to QR, and QP = NO, we can use the properties of similar triangles.
Considering triangles PNO and PQR, they are similar since they share the same angle at P and have parallel lines (NO and QR).
From this similarity, we can set up a proportion:
[tex]\(\frac{QP}{PN} = \frac{QR}{PO}\)[/tex]
Substitute the given values: QR = 10, NP = 21, QP = NO = NP.
[tex]\(\frac{QP}{21} = \frac{10}{PO}\)[/tex]
Now, solving for PO:
[tex]\(PO = \frac{10 \times 21}{QP} = \frac{210}{QP}\)[/tex]
Given that QP = NP = 21:
[tex]\(PO = \frac{210}{21} = 10\)[/tex]
