If triangle DEF is similar to triangle XYZ, and the lengths of DE and XY are 4 c

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What’s inside this PDF?

Question: If triangle DEF is similar to triangle XYZ, and the lengths of DE and XY 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 two similar triangles is the square of the ratio of their corresponding sides. Thus, (4/8)² = 1/4.

If triangle DEF is similar to triangle XYZ, and the lengths of DE and XY are 4 c

Practice Questions

If triangle DEF is similar to triangle XYZ, and the lengths of DE and XY 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 XYZ, and the lengths of DE and XY 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 XY = 8 cm.
Step 2: Find the ratio of the lengths of the corresponding sides. This is done by dividing DE by XY: 4 cm / 8 cm.
Step 3: Simplify the ratio from Step 2. 4 cm / 8 cm = 1/2.
Step 4: To find the ratio of the areas of the triangles, square the ratio of the sides from Step 3. (1/2)² = 1/4.
Step 5: Conclude that the ratio of the areas of triangle DEF to triangle XYZ 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 DEF is similar to triangle XYZ, and the lengths of DE and XY are 4 c

What’s inside this PDF?

If triangle DEF is similar to triangle XYZ, and the lengths of DE and XY are 4 c

Practice Questions

Questions & Step-by-Step Solutions

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