A triangle with sides of lengths 9,22 , and 24 is a right triangle.
A. True
B. False

Question

A triangle with sides of lengths 9,22 , and 24 is a right triangle. A. True B. False

UpStudy AI · Accepted Answer

To determine if a triangle with sides of lengths 9, 22, and 24 is a right triangle, we can use the Pythagorean theorem. According to the theorem, a triangle is a right triangle if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides.

Let's identify the sides:
- The longest side is 24.
- The other two sides are 9 and 22.

Now, we will check if the following equation holds:

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

where $$c$$ is the longest side (24), and $$a$$ and $$b$$ are the other two sides (9 and 22).

Calculating:

1. $$c^2 = 24^2$$
2. $$a^2 = 9^2$$
3. $$b^2 = 22^2$$

Now, let's perform the calculations.

$$
c^2 = 24^2 = 576
$$
$$
a^2 = 9^2 = 81
$$
$$
b^2 = 22^2 = 484
$$

Now, we will check if $$c^2 = a^2 + b^2$$:

$$
a^2 + b^2 = 81 + 484 = 565
$$

Now we compare:

$$
c^2 = 576 \quad \text{and} \quad a^2 + b^2 = 565
$$

Since $$576 \neq 565$$, the triangle is not a right triangle.

Thus, the answer is:

B. False
The triangle is not a right triangle, so the answer is B. False.

A triangle with sides of lengths 9,22 , and 24 is a right triangle.
A. True
B. False

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Geometry Questions