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In A PQR, point Mis on PQ, and point N is on QR, so that MN ||PR. It is given that QN = 2cm, NR - 8cm, and PR = 15cm. What is the length of MN? а. 3.75 cm b. 3 cm c.9 cm d. 7.5 cm

In A PQR Point Mis On PQ And Point N Is On QR So That MN PR It Is Given That QN 2cm NR 8cm And PR 15cm What Is The Length Of MN А 375 Cm B 3 Cm C9 Cm D 75 Cm class=

Sagot :

To answer this question, we can proceed as follows:

As we can see from the above figure, the triangles PQR and MQN are similar triangles. If they are similar, then their corresponding sides are in proportion. Then, we have:

[tex]\frac{PR}{MN}=\frac{RQ}{NQ}\Rightarrow\frac{15}{MN}=\frac{10}{2}[/tex]

Then, we need to solve the equation for MN, then we have:

[tex]\frac{15}{MN}=5\Rightarrow\frac{MN}{15}=\frac{1}{5}\Rightarrow MN=\frac{15}{5}\Rightarrow MN=3\operatorname{cm}[/tex]

Therefore, the value for the side MN is 3 cm (option b).

View image KaylynneV363543
View image KaylynneV363543
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