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

Answer 1

To use the Pythagorean theorem, we must first determine whether the triangle is a right triangle. The theorem states that in a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse.

Let's denote the sides of the triangle as follows:

• Side $a=17$ cm (one leg)
• Side $b=x$ cm (the other leg)
• Side $c=52$ cm (the hypotenuse)

Given that $c$ (52 cm) is longer than both $a$ and $b$, we can apply the Pythagorean theorem:

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

Substituting the known values:

$${17}^2+x^2={52}^2$$

Calculating the squares:

$$289+x^2=2704$$

Now, isolate $x^2$:

$$x^2=2704-289$$

$$x^2=2415$$

Taking the square root of both sides to solve for $x$:

$$x=\sqrt{2415}$$

Calculating the square root:

$$x\approx 49.15,\text{cm}$$

Thus, $x$ is approximately $49.15,\text{cm}$.