pll tell me this ans
Answers
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I could help you if known
Answer:
29
Step-by-step explanation:
n triangle XYZ, XM is a median if XY= 20, XZ = 21 and XM = 14.5
To find:
YZ
Solution:
We know that → a median from a vertex of a triangle bisects its third side.
∴ YM = ZM = \frac{1}{2} YZ21YZ
Apollonius theorem → \boxed{\bold{AB^2 + AC^2 = 2(AD^2 + BD^2)}} [considering\:AD \:is \:the\:median\:of\:\triangle ABC]AB2+AC2=2(AD2+BD2)[consideringADisthemedianof△ABC]
Now, using the above Apollonius theorem for Δ XYZ where XM is the median, we get
XY^2 + XZ^2 = 2 [XM^2+(\frac{YZ}{2} )^2]XY2+XZ2=2[XM2+(2YZ)2]
on substituting the values of XY = 20, XZ = 21 and XM = 14.5
\implies 20^2 + 21^2 = 2 [14.5^2+\frac{YZ^2}{4} ]⟹202+212=2[14.52+4YZ2]
\implies 841 = 2 [210.25+\frac{YZ^2}{4} ]⟹841=2[210.25+4YZ2]
\implies 841 = 420.5 +\frac{YZ^2}{2}⟹841=420.5+2YZ2
\implies \frac{YZ^2}{2} = 420.5⟹2YZ2=420.5
\implies YZ^2 = 841⟹YZ2=841
\implies \bold{YZ = 29}⟹YZ=29
Thus, the value of YZ is → 29.