Question

In the figure below, ABC is similar to XYZ . What is the length of ZX ? Enter only the number as an integer or decimal. An image shows two similar right triangles, A B C and X Y Z. Triangle A B C is smaller than triangle X Y Z. In triangle A B C, side A B is 2, side B C is 4, and side C A is 3. In triangle X Y Z, side X Y is 7, side Y Z is 14, and side Z X is labeled N.

Answer 1

Given:

Triangle ABC is similar to triangle XYZ.

In triangle ABC AB=2, BC=4, CA=3.

In triangle XYZ, XY=7, YZ=14, ZX=N.

To find:

The length of ZX.

Solution:

If two triangles are similar, then their corresponding sides are proportional.

Since $\Delta ABC\sim \Delta XYZ$, therefore

$\dfrac{AB}{XY}=\dfrac{BC}{YZ}=\dfrac{CA}{ZX}$

$\dfrac{2}{7}=\dfrac{4}{14}=\dfrac{3}{N}$

$\dfrac{2}{7}=\dfrac{2}{7}=\dfrac{3}{N}$

$\dfrac{2}{7}=\dfrac{3}{N}$

On cross multiplication, we get

$2\times N=3\times 7$

$2N=21$

Divide both sides by 2.

$N=\dfrac{21}{2}$

$N=10.5$

Therefore, the length of side ZX is 10.5 units.