If triangle DEF is similar to triangle XYZ and the ratio of their corresponding

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Question: If triangle DEF is similar to triangle XYZ and the ratio of their corresponding sides is 2:3, what is the ratio of their areas?

Options:

Correct Answer: 4:9

Solution:

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2/3)² = 4/9.

If triangle DEF is similar to triangle XYZ and the ratio of their corresponding sides is 2:3, what is the ratio of their areas?

If triangle DEF is similar to triangle XYZ and the ratio of their corresponding sides is 2:3, what is the ratio of their areas?

Step 1: Understand that triangle DEF is similar to triangle XYZ, which means their shapes are the same but their sizes are different.
Step 2: Note the ratio of their corresponding sides, which is given as 2:3.
Step 3: Recognize that to find the ratio of their areas, you need to square the ratio of their corresponding sides.
Step 4: Calculate the square of the ratio 2:3. This means you take (2/3) and multiply it by itself: (2/3) * (2/3).
Step 5: Perform the multiplication: 2 * 2 = 4 (for the numerator) and 3 * 3 = 9 (for the denominator).
Step 6: Write the result as a fraction: the ratio of the areas is 4/9.

Similarity of Triangles – Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.
Area Ratio of Similar Figures – The ratio of the areas of similar figures is equal to the square of the ratio of their corresponding linear dimensions (sides).