Question

Given the following lengths, find the length of side CD to the nearest tenth.

AD = 12, AB = 20, BC = 25
a) CD ≈ 13.4
b) CD ≈ 16.2
c) CD ≈ 18.4
d) CD ≈ 22.1

Answer 1

To find the length of side CD in triangle ABC, we can use the Pythagorean theorem. Substituting the given values, we calculate AC and then find CD by subtracting AD from AC. The approximate length of side CD is 20.0 units.

Step-by-step explanation:

To find the length of side CD, we can use the Pythagorean theorem. In triangle ABC, AB = 20 and BC = 25. By applying the Pythagorean theorem, we have AC^2 = AB^2 + BC^2. Substituting the given values, we get AC^2 = 20^2 + 25^2 = 400 + 625 = 1025. Taking the square root of both sides, we find AC ≈ √1025 ≈ 32.0. To find CD, subtract AD from AC: CD = AC - AD = 32.0 - 12 = 20.0. Therefore, the length of side CD is approximately 20.0 units.