If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE a

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Question: If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE 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 = (1/2)² = 1/4.

If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE a

Practice Questions

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

Questions & Step-by-Step Solutions

If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE 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 similar triangles. Here, AB = 4 cm and DE = 8 cm.
Step 2: Find the ratio of the lengths of the sides. This is done by dividing the length of side AB by the length of side DE: 4 cm / 8 cm.
Step 3: Simplify the ratio from Step 2. 4 cm / 8 cm simplifies to 1/2.
Step 4: To find the ratio of the areas of the triangles, square the ratio of the sides found in Step 3. (1/2)² = 1/4.
Step 5: Conclude that the ratio of the areas of triangle ABC to triangle DEF is 1/4.

Similarity of Triangles – Understanding that similar triangles have proportional sides and that the ratio of their areas is the square of the ratio of their corresponding sides.
Area Ratio Calculation – Calculating the area ratio using the formula that relates the ratio of sides to the ratio of areas.

If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE a

What’s inside this PDF?

If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE a

Practice Questions

Questions & Step-by-Step Solutions

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