Question

The sides of $\Delta \text{ABC}$ are 6 cm, 8 cm and 10 cm. Find the perimeter of the larger triangle which is similar to $\Delta \text{ABC}$ if the ratio of corresponding sides is 2.
[2 marks]
[Similar Triangles]

Answer 1

Solution:
Let’s assume the triangle similar to $\Delta \text{ABC}$ to be $\Delta \text{XYZ}$.
Given that the ratio of corresponding sides is 2.

So, $\frac{XY}{AB}=\frac{YZ}{BC}=\frac{XZ}{AC}=2$

The sides of $\Delta \text{ABC}$ are 6 cm, 8 cm and 10 cm.
Hence,
$\Rightarrow \frac{XY}{6}=\frac{YZ}{8}=\frac{XZ}{10}=2\left[1mark\right]$
$\Rightarrow XY=12cm,YZ=16cm$ and $XZ=20cm.$

The perimeter of $\Delta \text{XYZ}$ is $XY+YZ+XZ=12+16+20=48\left[1mark\right]$