In Delta XYZ,A, B and C are the midpoints of | vedclass

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(D) According to the Midpoint Theorem,the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half the

Vedclass · Accepted Answer

$32$

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(D) According to the Midpoint Theorem,the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side.Given that $A, B,$ and $C$ are midpoints of $XY, YZ,$ and $XZ$ respectively:$AB = \frac{1}{2} XZ \implies XZ = 2 	imes AB = 2 	imes 5.2\, cm = 10.4\, cm$$BC = \frac{1}{2} XY \implies XY = 2 	imes BC = 2 	imes 4.3\, cm = 8.6\, cm$$AC = \frac{1}{2} YZ \implies YZ = 2 	imes AC = 2 	imes 6.5\, cm = 13.0\, cm$The perimeter of $\Delta XYZ = XY + YZ + XZ = 8.6\, cm + 13.0\, cm + 10.4\, cm = 32.0\, cm$.

In $\Delta XYZ$,$A, B$ and $C$ are the midpoints of $XY, YZ$ and $XZ$ respectively. If $AB = 5.2\, cm$,$BC = 4.3\, cm$ and $AC = 6.5\, cm$,then find the perimeter of $\Delta XYZ$ in $cm$.

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