Question: a) Work out the length of the hypotenuse, $x$, for the triangle below.
b) Calculate the perimeter of the triangle.
15 cm
20 cm
$x$
Not drawn accurately
Graph/shape: A right-angled triangle in the center-bottom of the page, with a vertical left side labeled 15 cm, a horizontal base labeled 20 cm, and a slanted hypotenuse labeled $x$. position_hint \in \{center, bottom-left, bottom-right\} = center
1. **State the problem:** We have a right-angled triangle with legs of lengths $15$ cm and $20$ cm, and hypotenuse $x$. We need to find $x$ and then calculate the perimeter.
2. **Formula used:** For a right-angled triangle, the Pythagorean theorem states:
$$x^2 = a^2 + b^2$$
where $a$ and $b$ are the legs, and $x$ is the hypotenuse.
3. **Calculate the hypotenuse:**
$$x^2 = 15^2 + 20^2$$
$$x^2 = 225 + 400$$
$$x^2 = 625$$
4. **Find $x$ by taking the square root:**
$$x = \sqrt{625}$$
$$x = 25$$
5. **Calculate the perimeter:**
The perimeter $P$ is the sum of all sides:
$$P = 15 + 20 + x$$
$$P = 15 + 20 + 25$$
$$P = 60$$
**Final answers:**
- Hypotenuse length $x = 25$ cm
- Perimeter $P = 60$ cm