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triangle abc is similar to triangle def solve for both unknown sides

Triangle Abc Is Similar To Triangle Def Solve For Both Unknown Sides class=

Sagot :

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.

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