In the image, we see a right-angled triangle labeled with dimensions. The triangle is divided into two smaller triangles, $A$ and $B$, where:

• The total base of the large triangle is 16 cm.
• The perpendicular height from the base to the top vertex is 12 cm.
• The base of the smaller triangle labeled $B$ is 5 cm.
• The remaining part of the base (under triangle $A$) is $16 - 5 = 11$ cm.

To analyze this triangle:

1. Area of the Triangle: The area of the large triangle can be calculated using the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area} = \frac{1}{2} \times 16 \, \text{cm} \times 12 \, \text{cm} = 96 \, \text{cm}^2$

2. Right Triangle Relations: Since the smaller triangles are right-angled, you can apply the Pythagorean theorem to each.

   For triangle $A$: $\text{Hypotenuse}^2 = 11^2 + 12^2 = 121 + 144 = 265$ So, the hypotenuse of triangle $A$ is $\sqrt{265} \approx 16.28 \, \text{cm}$.

   For triangle $B$: $\text{Hypotenuse}^2 = 5^2 + 12^2 = 25 + 144 = 169$ So, the hypotenuse of triangle $B$ is $\sqrt{169} = 13 \, \text{cm}$.

Would you like more details on these calculations, or explanations on a specific part of the problem?

Here are 5 related questions:

1. How would you find the perimeter of triangle $A$?
2. What would be the perimeter of triangle $B$?
3. How can you verify the areas of the smaller triangles?
4. What are the angles of triangle $A$ besides the right angle?
5. Can you find the trigonometric ratios for triangle $B$?

Tip: In right triangles, the Pythagorean theorem is very useful for determining missing sides when two sides are known.