Question

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 \( 49.15 \, \text{cm} \).