Question

in a figure, L,M,N are mid points of the sides of XY,XZ and YZ respectively of triangle XYZ.If XY=4.4cm,YZ=5.6cm and XZ=4.8cm then find the perimeter of triangle LMN​

Answer 1

Answer:

It is given that L, M and N are mid-point of the side PQ, PR and QR respectively of ΔPQR. If PQ=4.4cm, QR=5.6cm and PR=4.8 cm.

Since, L, M and N are mid-point of the side PQ, PR and QR respectively of ΔPQR., therefore

LM=\frac{1}{2}(QR)LM=

2

1

(QR)

LM=\frac{1}{2}(5.6)=2.8cmLM=

2

1

(5.6)=2.8cm ,

LN=\frac{1}{2}(PR)=\frac{1}{2}(4.8)=2.4cmLN=

2

1

(PR)=

2

1

(4.8)=2.4cm

and MN=\frac{1}{2}(PQ)=\frac{1}{2}(4.4)=2.2cmMN=

2

1

(PQ)=

2

1

(4.4)=2.2cm

Thus, the perimeter of ΔLMN will be given as:

P=LM+LN+MNP=LM+LN+MN

P=2.8+2.4+2.2P=2.8+2.4+2.2

P=7.4 cmP=7.4cm

Therefore, the perimeter of ΔLMN is 7.4 cm.