Question: User: 1
5 cm
8 cm
x cm
NOT TO
SCALE
Calculate the value of x.
[3]
graph_shape: right triangle; math: 5 cm and x cm are the perpendicular sides, 8 cm is the hypotenuse; position_hint: top-left
1. **Problem:** Calculate the value of $x$ in a right triangle where the two perpendicular sides are $5$ cm and $x$ cm, and the hypotenuse is $8$ cm.
2. **Formula:** Use the Pythagorean theorem for right triangles:
$$a^2 + b^2 = c^2$$
where $a$ and $b$ are the perpendicular sides and $c$ is the hypotenuse.
3. **Apply values:**
$$5^2 + x^2 = 8^2$$
4. **Calculate squares:**
$$25 + x^2 = 64$$
5. **Isolate $x^2$:**
$$x^2 = 64 - 25$$
$$x^2 = 39$$
6. **Find $x$ by taking the square root:**
$$x = \sqrt{39}$$
7. **Simplify the square root:**
$39$ is $3 \times 13$, no perfect square factors, so
$$x \approx 6.24$$
**Final answer:**
$$x \approx 6.24 \text{ cm}$$