If triangle DEF is similar to triangle XYZ and the length of DE is 6 cm, what is

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Question: If triangle DEF is similar to triangle XYZ and the length of DE is 6 cm, what is the length of XY if the ratio of similarity is 2:3?

Options:

Correct Answer: 9 cm

Solution:

Using the ratio of similarity, if DE = 6 cm, then XY = (3/2) * 6 = 9 cm.

If triangle DEF is similar to triangle XYZ and the length of DE is 6 cm, what is the length of XY if the ratio of similarity is 2:3?

If triangle DEF is similar to triangle XYZ and the length of DE is 6 cm, what is the length of XY if the ratio of similarity is 2:3?

Step 1: Understand that triangle DEF is similar to triangle XYZ, which means their sides are in proportion.
Step 2: Identify the given length of side DE, which is 6 cm.
Step 3: Note the ratio of similarity, which is 2:3. This means for every 2 units in triangle DEF, there are 3 units in triangle XYZ.
Step 4: Set up the proportion using the ratio. If DE corresponds to XY, we can write it as DE/XY = 2/3.
Step 5: Substitute the known value of DE into the proportion: 6/XY = 2/3.
Step 6: To find XY, cross-multiply: 2 * XY = 6 * 3.
Step 7: Calculate the right side: 6 * 3 = 18, so we have 2 * XY = 18.
Step 8: Divide both sides by 2 to solve for XY: XY = 18 / 2.
Step 9: Calculate the final value: XY = 9 cm.

Similarity of Triangles – Triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.
Ratio of Similarity – The ratio of the lengths of corresponding sides of similar triangles is constant and can be used to find unknown side lengths.