Solve for X on a triangle with three sides, 1 side is 52 cm, the second side is 17 cm and the third side is x, calculate x using the Pythagorean Theorem 17 is the hypotenuse

Answer 1

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:

1. Calculate ${17}^2$: $${17}^2=289$$

2. Calculate ${52}^2$: $${52}^2=2704$$

3. Substitute these values into the equation:

$$x^2+289=2704$$

4. Solve for $x^2$:

$$x^2=2704-289=2415$$

5. 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.