In ΔABC, X and Y are the midpoints of the sides AB and AC, respectively, and AB = AC = 10 cm, and BC = 12 cm. The perpendicular drawn from X meets BC at point P. Find the area of ΔXBP.
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Answer:
XY is parallel to BC
Step-by-step explanation:
Given
\frac{Ax}{AB}=\frac{1}{4}ABAx=41
AY=2\text{ cm}AY=2 cm
YC=6\text{ cm}YC=6 cm
AC=AY+YC=2+6=8\text{ cm}AC=AY+YC=2+6=8 cm
The ratio between AY and AC
\begin{gathered}\frac{AY}{AC}=\frac{2}{8}\\\\\therefore\frac{AY}{YC}=\frac{1}{4}\end{gathered}ACAY=82∴YCAY=41
As per the side splitter theorem if a line intersect the other two sides of a triangle and the line divides those two sides proportionally then the line is parallel to the third side of a triangle.
Therefore,
XY\parallel BCXY∥BC
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