Question
Download Solution PDF\(\Delta XYZ \sim \Delta GST\) and XY ∶ GS = 2 ∶ 3, XV is the median to the side YZ, and GD is the median to the side ST. The value of \(({\frac{{YV}}{{SD}}}) ^2\) is _______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
XY ∶ GS = 2 ∶ 3
Concept used:
If two sides and a median bisecting the third side of a triangle are respectively proportional to the corresponding sides and the median of another triangle, then two triangles are similar.
Calculation:
As \(\Delta XYZ \sim \Delta GST\)
So, \(({\frac{{YV}}{{SD}}}) ^2\) = \(({\frac{{XY}}{{GS}}}) ^2\)
⇒ \(({\frac{{2}}{{3}}}) ^2\)
⇒ \(\frac{4}{9}\)
∴ The value of \(({\frac{{YV}}{{SD}}}) ^2\) is \(\frac{4}{9}\).
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