Select 3 side lengths that can form a right triangle. 12 centimeters 14 centimeters 16 centimeters 30 centimeters 32 centimeters 34 centimeters Submit

Question

UpStudy AI · Accepted Answer

To determine which set of side lengths can form a right triangle, we can use the Pythagorean theorem. According to this theorem, for three lengths $$a$$, $$b$$, and $$c$$ (where $$c$$ is the longest side), the following condition must hold:

$$
a^2 + b^2 = c^2
$$

Let's check both sets of side lengths:

### Set 1: 12 cm, 14 cm, 16 cm
1. Identify the longest side: $$c = 16$$ cm, $$a = 12$$ cm, $$b = 14$$ cm.
2. Calculate $$a^2 + b^2$$ and $$c^2$$:
   - $$a^2 + b^2 = 12^2 + 14^2 = 144 + 196 = 340$$
   - $$c^2 = 16^2 = 256$$

Since $$340 \neq 256$$, this set does not form a right triangle.

### Set 2: 30 cm, 32 cm, 34 cm
1. Identify the longest side: $$c = 34$$ cm, $$a = 30$$ cm, $$b = 32$$ cm.
2. Calculate $$a^2 + b^2$$ and $$c^2$$:
   - $$a^2 + b^2 = 30^2 + 32^2 = 900 + 1024 = 1924$$
   - $$c^2 = 34^2 = 1156$$

Since $$1924 \neq 1156$$, this set does not form a right triangle.

### Conclusion
Neither set of side lengths can form a right triangle.
Neither set of side lengths (12 cm, 14 cm, 16 cm) nor (30 cm, 32 cm, 34 cm) can form a right triangle.

Select 3 side lengths that can form a right triangle. 12 centimeters 14 centimeters 16 centimeters 30 centimeters 32 centimeters 34 centimeters Submit

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Geometry Questions