Question

In ∆LMN, if LM = 10cm, angle LNM = 90°, angle LMN = 30°, then NM=?

5√2cm

5cm

10√3cm

5√3cm

​

Answer 1

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LM=9cm

MN=12cm

LN=15cm

∴PM=4.5cm

QN=7.5cm

And we know that the line joining the mid points of the two sides of a triangle is parallel to the third side and is equal to half of it.

∴PQ= 1/2

MN=6cm

(i)Perimeter of trapezium MNQP=(4.5+7.5+12+6)

=24+6

=30cm

(ii)Area of trapezium= 1/2

×(sum of parallel sides)× (height)

=1/2×(12+6)×4.5

=9×4.5

=40.5cm.