If triangle GHI is similar to triangle JKL and the ratio of their corresponding

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

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

Step 1: Understand that triangle GHI is similar to triangle JKL, which means they have the same shape but different sizes.
Step 2: Note the ratio of their corresponding sides, which is given as 2:3.
Step 3: Recognize that the ratio of the areas of similar triangles is found by squaring the ratio of their corresponding sides.
Step 4: Calculate the square of the ratio of the sides: (2/3)².
Step 5: Perform the calculation: (2/3)² = 4/9.
Step 6: Conclude that the ratio of the areas of triangle GHI to triangle JKL 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).