Question: Work out the perimeter of this
triangle?
Give your answer to 1 d.p.
9 cm
2 cm
12 cm
Not drawn accurately
Graph/shape: a triangle in the center with a vertical height of 9 cm dropping to the base; the base is split into 2 cm on the left and 12 cm on the right, so the total base is 14 cm. Position_hint: center
1. **State the problem:** We need to find the perimeter of a triangle with a vertical height of $9$ cm and a base split into two segments of $2$ cm and $12$ cm, so the total base length is $14$ cm.
2. **Identify the sides:** The base is $14$ cm. The height is $9$ cm, which forms a right triangle with the base segments.
3. **Find the lengths of the two other sides:**
- Left side length using Pythagoras theorem: $$\text{left side} = \sqrt{9^2 + 2^2} = \sqrt{81 + 4} = \sqrt{85}$$
- Right side length: $$\text{right side} = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225}$$
4. **Calculate the exact lengths:**
- Left side: $$\sqrt{85} \approx 9.22$$ cm
- Right side: $$\sqrt{225} = 15$$ cm
5. **Calculate the perimeter:**
$$\text{Perimeter} = 14 + 9.22 + 15 = 38.22$$ cm
6. **Round to 1 decimal place:**
$$38.22 \approx 38.2$$ cm
**Final answer:** The perimeter of the triangle is $38.2$ cm.