To solve for \( x \) in a triangle using the Pythagorean theorem, we first need to identify the sides of the triangle correctly. The Pythagorean theorem is stated as:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse (the longest side), and \( a \) and \( b \) are the lengths of the other two sides.
From your description, it seems that you have the following sides:
- One side \( a = x \)
- Another side \( b = 52 \) cm
- The hypotenuse \( c = 17 \) cm
However, you cannot have a hypotenuse shorter than the other sides in a right triangle. Since the hypotenuse must be the longest side, we must verify this situation.
If \( 17 \) cm is the hypotenuse, it must be longer than both \( x \) and \( 52 \) cm. Since \( 52 \) cm is greater than \( 17 \) cm, the situation provided cannot represent a valid right triangle with \( 17 \) as the hypotenuse.
Likely, the correct hypotenuse must be \( 52 \) cm. Therefore, we should reapply the Pythagorean theorem with \( 52 \) as the hypotenuse.
So, the equation should be revised as:
\[ x^2 + 17^2 = 52^2 \]
Now let's calculate it:
-
Calculate \( 17^2 \): \[ 17^2 = 289 \]
-
Calculate \( 52^2 \): \[ 52^2 = 2704 \]
-
Substitute these values into the equation:
\[ x^2 + 289 = 2704 \]
- Solve for \( x^2 \):
\[ x^2 = 2704 - 289 = 2415 \]
- Take the square root of both sides to find \( x \):
\[ x = \sqrt{2415} \approx 49.15 \text{ cm} \]
So, the value of \( x \) is roughly \( 49.15 \) cm.
1 answer