Question

select the correct answer from each drop - down menu. △abc has side lengths of 10 units, 20 units, and 24 units. △xyz is similar to △abc, and the length of its longest side is 60 units. the perimeter of △xyz is <units. if the height of △abc, with respect to its longest side being the base, is 8 units, the area of △xyz is <square units. reset next

Explanation:

Step1: Find the similarity ratio

Since $\triangle XYZ$ is similar to $\triangle ABC$, and the longest - side of $\triangle ABC$ is 24 units and that of $\triangle XYZ$ is 60 units. The similarity ratio $k=\frac{60}{24}=\frac{5}{2}$.

Step2: Find the other side - lengths of $\triangle XYZ$

The other side - lengths of $\triangle ABC$ are 10 units and 20 units. The corresponding side - lengths of $\triangle XYZ$ are $10\times\frac{5}{2} = 25$ units and $20\times\frac{5}{2}=50$ units.

Step3: Calculate the perimeter of $\triangle XYZ$

The perimeter of $\triangle XYZ$ is $25 + 50+60=135$ units.

Step4: Calculate the area of $\triangle ABC$

The area of $\triangle ABC$ with base $b = 24$ units and height $h = 8$ units is $A_{ABC}=\frac{1}{2}\times24\times8 = 96$ square units.

Step5: Calculate the area of $\triangle XYZ$

For similar triangles, the ratio of their areas is $k^{2}$. Since $k=\frac{5}{2}$, $k^{2}=\frac{25}{4}$. So the area of $\triangle XYZ$ is $A_{XYZ}=96\times\frac{25}{4}=600$ square units.

Answer:

The perimeter of $\triangle XYZ$ is 135 units, and the area of $\triangle XYZ$ is 600 square units.