Question

construct a right triangle:∆LMN in which MN=5.9cm LM=8.4cm and ∆N=90°​

Answer 1

Step-by-step explanation:

ANSWER

Since P and Q are mid-points of LM and LN.

LM

LP

=

LN

LQ

=

2

1

In △LPQ and △LMN

LM

LP

=

LN

LQ

∠PLQ=∠MLN(Common)

=>△LPQ∼△LMN(ByS.A.Ssimilaritycriterion)

∴

MN

PQ

=

LM

LP

=

2

1

(CPST)

or

MN

PQ

=

2

1

12

PQ

=

2

1

(∵MN=12cm)

PQ=

2

12

=6cm

PM=

2

1

LM=

2

9

=4.5cm [Since P and Q are mid-points of LM and LN]

$$QN=\dfrac { 1 }{ 2 } LN=\dfrac { 15 }{ 2 } =7.5cm\\ MN=12cm\\ $$

(i) Perimeter of trapezium MNQP

=MN+NQ+PQ+PM

=12+7.5+6+4.5

=30cm

(ii)Area of Trapezium MNQP

=Base×Height

=MN×PM

=12×4.5

=54cm

2