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 3:5, what is the ratio of their areas?

Options:

Correct Answer: 9:25

Solution:

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (3/5)² = 9/25.

If triangle GHI is similar to triangle JKL and the ratio of their corresponding sides is 3:5, what is the ratio of their areas?

If triangle GHI is similar to triangle JKL and the ratio of their corresponding sides is 3:5, 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 3:5.
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 3:5. This means you take (3/5) and multiply it by itself: (3/5) * (3/5).
Step 5: Perform the multiplication: 3 * 3 = 9 (for the numerator) and 5 * 5 = 25 (for the denominator).
Step 6: Write the result as a fraction: 9/25. This is the ratio of the areas of triangle GHI to triangle JKL.

Similarity of Triangles – Triangles that have the same shape but may differ in size, with corresponding angles equal and corresponding sides 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).