Mathematics: 5. * in a parallogram abcd, p divides ab in the ratio 2 : 5 and q divides dc in the ratio 3 : 2. if ac and pq intersect at r, ﬁnd the ratios ar : rc and pr : rq

5. * in a parallogram abcd, p divides ab in the

gwoodbyrne

03.01.2022

Answer

AR: RC = 1 : 1 and PR : RQ = 1 : 1

Step-by-step explanation:

Using figure 1 as shown below.

$In\triangle ARP and \triangle QRC.$

$\angle ARP =\angle QRC (vertically\ opposite\ angles)$

$\angle PAR =\angle QCR \ (\because AB \parallel CD)$

$\therefore \triangle ARP\sim \triangle QRC$ (by AA similarity)

$\therefore\frac{AP}{AR} =\frac{QC}{RC}$

$\frac{2x}{AR} =\frac{2x}{RC}$

AR: RC = 1: 1

In the similar way,

$\frac{QC}{RQ} =\frac{AP}{PR}$

$\frac{PR}{RQ} = \frac{AP}{QC} =\frac{2x}{2x}$

Therefore, PR: RQ = 1: 1

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tiaemrich146

01.06.2023

$16.25

Step-by-step explanation:

$5 + (15x$0.75) = $16.25

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