Question

The sides of a triangle measure 2, 3, and 4. If the smallest side of a similar triangle measures 8, then the measure of the largest side is

Answer 1

The length of the sides of the smaller triangles is 2, 2, and4.

The smallest length of the smaller triangle is: 2

The length of the largest side of the given small triangle is: 4

The smallest length of the big triangle is: 8

The small triangle and the large triangle are similar triangles. The ratio of corresponding sides of similar triangles is equal.

`\begin{gathered} \frac{Small\text{ side of small triangle}}{\text{Small side of big triangle}}=\frac{Large\text{ side of small triangle}}{\text{Largest side of big triangle}} \\ (2)/(8)=\frac{4}{\text{Largest side of big triangle}} \\ \text{Largest side of big triangle}=4*(8)/(2) \\ =16 \end{gathered}`

Thus, the length of the largest side of the big triangle is 16.