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liq [111]
3 years ago
5

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

Mathematics
1 answer:
Serhud [2]3 years ago
7 0

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

\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{CA}{FD}

\dfrac{6}{x}=\dfrac{16}{32}=\dfrac{15}{y}

\dfrac{6}{x}=\dfrac{1}{2}=\dfrac{15}{y}

Now,

\dfrac{6}{x}=\dfrac{1}{2}

6\times 2=1\times x

12=x

Similarly,

\dfrac{1}{2}=\dfrac{15}{y}

1\times y=15\times 2

y=30

Therefore, the measure of unknown sides are x = 12 m and y = 30 m.

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