Given:
Triangles ABC and DEF are similar triangles.
AB = 6 m, BC = 16 m, CA = 15 m, DE = x, EF = 32 m, FD = y
To find:
The values of unknown sides, i.e., x and y.
Solution:
We know that the corresponding parts of similar triangles are proportional and triangles ABC and DEF are similar triangles, so
[tex]\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{CA}{FD}[/tex]
[tex]\dfrac{6}{x}=\dfrac{16}{32}=\dfrac{15}{y}[/tex]
[tex]\dfrac{6}{x}=\dfrac{1}{2}=\dfrac{15}{y}[/tex]
Now,
[tex]\dfrac{6}{x}=\dfrac{1}{2}[/tex]
[tex]6\times 2=1\times x[/tex]
[tex]12=x[/tex]
Similarly,
[tex]\dfrac{1}{2}=\dfrac{15}{y}[/tex]
[tex]1\times y=15\times 2[/tex]
[tex]y=30[/tex]
Therefore, the measure of unknown sides are x = 12 m and y = 30 m.
