Question

In A MNP Seg. QR || Seg. NP. If 3.2 QN 53 QM and QR = 6.4 then NP = 7
N
M
RP
(A) 11.7
(B) 17
(C) 10.4
(D) 15.9​

Answer 1

Given : ΔMNP Seg. QR || Seg. NP

3.2QN = 5.3QM

QR = 6.4

To Find :   NP

Solution :

Seg. QR || Seg. NP

=> ΔMQR ≈ ΔMNP  

=> QR/NP  = QM/MN

3.2QN = 5.3QM

=> QN/QM = 5.3/3.2

adding 1 both sides

=> (QN+ QM)/QM = 8.5/3.2

=> MN/QM = 8.5/3.2

=> QM/MN = 3.2/8.5

=> QR/NP  =  3.2/8.5

=> 6.4/NP  =  3.2/8.5

=> NP = 17

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Answer 2

Given:

In A MNP Seg. QR || Seg. NP

3.2 QN = 5.3 QM

QR = 6.4

To find:

NP

Solution:

It is given that,

3.2QN = 5.3QM

⇒  $\frac{QN}{QM} = \frac{5.3}{3.2}$

In Δ MRQ and Δ MPN, since seg QR // seg NP, so, we get

∠MRQ = ∠MPN [corresponding angles]

∠RMQ = ∠PMN  [common angle]

∴  Δ MRQ ~ Δ MPN [By AA similarity]

We know that → the corresponding sides of two similar triangles are proportional to each other.

∴ $\frac{QM}{MN} = \frac{QR}{NP}$

$\implies \frac{QM}{QN +QM} = \frac{QR}{NP}$

substituting the values of QM, QN and QR, we get

$\implies \frac{3.2}{5.3 +3.2} = \frac{6.4}{NP}$

$\implies \frac{3.2}{8.5} = \frac{6.4}{NP}$

$\implies NP = \frac{6.4 \times 8.5}{3.2}$

$\implies \bold{NP = 17}$

Thus, NP → option (B) → 17

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