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Observe a figura a seguir.



A medida de x, em centímetro, é

16.

18.

21.

24.

To solve for the length of \( x \) in the triangle, we can use the Pythagorean Theorem because the triangle contains a right angle.

The Pythagorean Theorem states that in a right triangle:

\[
a^2 + b^2 = c^2
\]

Where:
- \( a \) and \( b \) are the lengths of the legs of the triangle.
- \( c \) is the length of the hypotenuse.

In the given triangle:
- One leg is \( 7 \) cm.
- The other leg is \( x \).
- The hypotenuse is \( 25 \) cm.

Applying the Pythagorean Theorem:

\[
7^2 + x^2 = 25^2
\]

\[
49 + x^2 = 625
\]

Subtract 49 from both sides:

\[
x^2 = 625 - 49 = 576
\]

Taking the square root of both sides:

\[
x = \sqrt{576} = 24 \, \text{cm}
\]

So, the value of \( x \) is 24 cm.

Would you like any more details or explanations?

Here are five related questions for further exploration:

1. How would the length of \( x \) change if the hypotenuse were 30 cm instead of 25 cm?
2. Can the Pythagorean Theorem be used for non-right triangles? Why or why not?
3. If the shorter leg of the triangle was 9 cm instead of 7 cm, what would \( x \) be?
4. How would you find the area of this triangle?
5. What other methods could you use to solve for \( x \) in this triangle?

**Tip:** Always check that the triangle is a right triangle before applying the Pythagorean Theorem.

Learn how to find the length of x in a right triangle using the Pythagorean Theorem. This problem involves a triangle with sides 7 cm, x cm, and a hypotenuse of 25 cm. Step-by-step solution provided.

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