High School

We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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.

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

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]

Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada