Question

What is triangle LMN, LwhaM = 8cm, MN = 6cm and LMN = 90°X and Y are the midpoints of MN and LN respectively.Find YXN and YN.​

Answer 1

Step-by-step explanation:

for first condition ,

∆LMN is right angled triangle.. ......(LMN=90°)........given

so therefore,by using theorem of pythagorous,

LN2= MN2+ LM2

=8×8 + 6×6

=64 + 36

=100

LN = √100

LN = 10cm

that is why ,

Y is midpoint of LN ...............given

so therefore,

LN= LY+YN

let,LY & YN be x

10 =x+x

10=2x

x =10÷2

x=5

YN=5

X is midpoint of MN,

MN =6cm

MX=XN=MN÷2

=6÷2

=3

XN=3cm

because of that we can give ,the LM is parallel to YX.

so therefore,

∆YXN is also right angled triangle.

YX2+NX2=YN2........by using thm of pythagorous

x2 +3×3 = 5×5

x 2+9 =25

x 2=25-9

x2=16

x=√16

x=4cm