If triangle DEF is similar to triangle XYZ and the length of DE is 4 cm and XY i

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Question: If triangle DEF is similar to triangle XYZ and the length of DE is 4 cm and XY is 8 cm, 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 XYZ and the length of DE is 4 cm and XY is 8 cm, what is the ratio of their areas?

If triangle DEF is similar to triangle XYZ and the length of DE is 4 cm and XY is 8 cm, 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. 4/8 simplifies to 1/2.
Step 4: To find the ratio of the areas of the triangles, square the ratio of the sides. (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 – 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.