Question

If PM 4.5 find the value of PQ

Answer 1

Answer:

Here, using the corollary of basic proportionally theorem which states that if a line passing through the two sides of the triangle cuts it proportionally, then the line is parallel to the third side. So,

(i)

QM

PM

=

4.5

4

=

9

8

NR

PN

=

4.5

4

=

9

8

∴

QM

PM

=

NR

PN

Thus, as MN cuts the sides PQ and PR proportionally, so MN∥QR.

∴ MN∥QR

(ii)

QM

PM

=

1.28−0.16

0.16

=

1.12

0.16

=

7

1

NR

PN

=

2.56−0.32

0.32

=

2.24

0.32

=

7

1

∴

QM

PM

=

NR

PN

Thus, as MN cuts the sides PQ and PR proportionally, so MN∥QR.

∴ MN∥QR