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Mathematics

Grade9

Easy

Question

Find the value of x for two similar triangles.

9
11
21
31

hint Hint:

If two triangles are similar, then the ratio of corresponding sides is equal to the ratio of the angle bisectors, altitudes, and medians of the two triangles. Find value of x by equating the ratios.

The correct answer is: 9

If two triangles are similar, then the ratio of corresponding sides is equal to the ratio of the angle bisectors, altitudes, and medians of the two triangles.
$fraction numerator E F over denominator A B end fraction equals fraction numerator D E over denominator C B end fraction$ (Corresponding sides are proportional)
$fraction numerator 21 over denominator 77 end fraction equals fraction numerator 30 over denominator 11 x plus 11 end fraction$
$21 left parenthesis 11 x plus 11 right parenthesis blank equals 77 cross times 30$
$x equals 9$
Therefore, value of x is 9.

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