Question

The areas of similar triangles ∆ABC and ∆DEF are equal. If the longest side of ∆DEF measures 25 units, what is the length of the longest side of ∆ABC

1. 5 Units
2. 25 Units
3. 50 Units
4. 75 Units

Answer 1

i think it is 2. 25, because it said their areas were equal

Answer 2

2) 25 units

Explanation:

Given: The areas of similar triangles ∆ABC and ∆DEF are equal.

By the definition of similar triangles, the corresponding angles must be equal but the side will be in proportion.

Here the areas of the triangles ABC and DEF are equal. Therefore, they must be a congruent triangles.

If the triangles are congruent, then its corresponding sides must be equal.

Therefore, the longest side of ΔABC is same as the longest side of ΔDEF.

So, the answer is 25 units.