In triangle DEF, DE = 12 cm, EF = 15 cm, and angle DEF = 90°. Triangle DEF is congruent to triangle XYZ. If YZ = 15 cm, then what is the length of XZ?

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Given triangle DEF with DE = 12 cm, EF = 15 cm, and angle DEF = 90°, triangle DEF is a right triangle with the right angle at E.

Step 1: Calculate the length of DF using the Pythagorean theorem:
DF² = DE² + EF² = 12² + 15² = 144 + 225 = 369
DF = √369 = √(9 × 41) = 3√41 cm

Step 2: Since triangle DEF is congruent to triangle XYZ, corresponding sides are equal in length.
Given YZ = 15 cm corresponds to EF = 15 cm.

Step 3: We need to find XZ, which corresponds to DF.
Therefore, XZ = DF = 3√41 cm.

Hence, the length of XZ is 3√41 cm.

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