Question

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

Answer 1

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.