If triangle DEF is similar to triangle GHI, and the lengths of DE and GH are 4 c

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Question: If triangle DEF is similar to triangle GHI, and the lengths of DE and GH are 4 cm and 8 cm respectively, what is the ratio of their areas?

Options:

Correct Answer: 1:4

Solution:

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (4/8)^2 = 1/4.

If triangle DEF is similar to triangle GHI, and the lengths of DE and GH are 4 c

Practice Questions

If triangle DEF is similar to triangle GHI, and the lengths of DE and GH are 4 cm and 8 cm respectively, what is the ratio of their areas?

Questions & Step-by-Step Solutions

If triangle DEF is similar to triangle GHI, and the lengths of DE and GH are 4 cm and 8 cm respectively, what is the ratio of their areas?

Step 1: Identify the lengths of the corresponding sides of the triangles. Here, DE = 4 cm and GH = 8 cm.
Step 2: Find the ratio of the lengths of the corresponding sides. This is done by dividing DE by GH: 4 cm / 8 cm = 1/2.
Step 3: To find the ratio of the areas of the triangles, square the ratio of the sides. So, (1/2)^2 = 1/4.
Step 4: Conclude that the ratio of the areas of triangle DEF to triangle GHI is 1/4.

Similarity of Triangles – Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.
Area Ratio of Similar Triangles – The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding side lengths.

If triangle DEF is similar to triangle GHI, and the lengths of DE and GH are 4 c

What’s inside this PDF?

If triangle DEF is similar to triangle GHI, and the lengths of DE and GH are 4 c

Practice Questions

Questions & Step-by-Step Solutions

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