Question

if two triangles are similar and one side of triangle a is twice the length of the corresponding side in triangle b, what is the ratio of their areas?
4:1
1:4
none of the other answer options are correct.
1:2
2:1

Explanation:

Step1: Recall the ratio of areas formula

For similar triangles, if the ratio of corresponding side lengths is \(k\), the ratio of their areas is \(k^{2}\).

Step2: Determine the ratio of side lengths

Given that one side of Triangle \(A\) is twice the length of the corresponding side in Triangle \(B\), so the ratio of side lengths \(k = 2\).

Step3: Calculate the ratio of areas

Using the formula \(k^{2}\), substitute \(k = 2\), we get \(2^{2}=4\). So the ratio of the area of Triangle \(A\) to the area of Triangle \(B\) is \(4:1\).

Answer:

A. \(4:1\)