The triangle ABC is right angled, as shown:

Right angled triangle ABC

If AB=15−−√
cm and AC=9
cm, calculate the length of BC, giving your answer in exact form.

Select one:

a.
46–√
cm


b.
66−−√
cm


c.
96−−√
cm


d.
8
cm

Given that triangle ABC is a right-angled triangle, we can use the **Pythagorean Theorem** to find the length of side \(BC\).

The Pythagorean Theorem states:
\[
AB^2 = AC^2 + BC^2
\]

Here:
- \( AB = \sqrt{15} \) cm (hypotenuse)
- \( AC = 9 \) cm (one of the legs)
- \( BC \) is the unknown side we need to calculate.

Let's apply the theorem:

\[
(\sqrt{15})^2 = AC^2 + BC^2
\]

Substituting the known values:

\[
15 = 9^2 + BC^2
\]
\[
15 = 81 + BC^2
\]
\[
BC^2 = 15 - 81 = -66
\]

It appears I made an error assuming \(AB\) was the hypotenuse. Let's reconsider the question.

Since \( \sqrt{15} \) is **not** the hypotenuse, the correct approach would be:

\[
AB^2 + AC^2 = BC^2
\]

Now, I'll solve for \(BC\).import math

# Given values
AB = math.sqrt(15)  # cm
AC = 9  # cm

# Using Pythagoras Theorem to calculate BC
BC_squared = AB**2 + AC**2
BC = math.sqrt(BC_squared)

BCThe length of side \( BC \) is approximately \( 9.8 \) cm.

However, the question asks for the exact form, so let's refine this and match it to one of the given options. The exact length of \( BC \) is:

\[
BC = \sqrt{96}
\]

Thus, the correct answer is:

**c. \( \sqrt{96} \) cm**

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you identify the hypotenuse in any right triangle?
2. Can the Pythagorean Theorem be applied to non-right triangles?
3. What are the possible simplifications for square roots like \( \sqrt{96} \)?
4. How do you calculate the area of a right-angled triangle?
5. How would the answer change if the triangle were not right-angled?

**Tip:** Always check whether you have identified the correct hypotenuse when using the Pythagorean Theorem.

Learn how to calculate the length of side BC in a right-angled triangle using the Pythagorean Theorem. Given AB = sqrt(15) cm and AC = 9 cm, find the exact length of BC. Suitable for students in Grades 7-9.

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