Question

a photograph of a triangular object and an enlargement are shown below. the length n of the missing side in the enlargement is ________ inches. (write the answer as a decimal.) the solution is

Explanation:

Step1: Identify similar - triangles property

Since the two triangles are similar, the ratios of corresponding sides are equal.
Let the side of length 4 in the small triangle correspond to the side of length 10 in the large triangle, and the side of length 3 in the small triangle correspond to the side of length $n$ in the large triangle.
The ratio of the sides is $\frac{10}{4}$.

Step2: Set up proportion

We have the proportion $\frac{n}{3}=\frac{10}{4}$.

Step3: Solve for $n$

Cross - multiply: $4n = 3\times10$.
So, $4n=30$.
Then, $n=\frac{30}{4}=7.5$.

Answer:

7.5