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Let's solve Question 9:

**Question 9:**
The base and height of a triangle are in the ratio 4:5. If the area is 640 sq. cm, find the base and height.

### Solution:

Let the base of the triangle be \( 4x \) and the height be \( 5x \).

The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Given:
\[
\text{Area} = 640 \, \text{sq. cm}
\]
Substituting the values for the base and height in terms of \(x\):
\[
640 = \frac{1}{2} \times (4x) \times (5x)
\]
Simplifying:
\[
640 = \frac{1}{2} \times 20x^2
\]
\[
640 = 10x^2
\]
Now solve for \(x^2\):
\[
x^2 = \frac{640}{10} = 64
\]
\[
x = \sqrt{64} = 8
\]

Now, substitute \(x = 8\) into the expressions for the base and height:
- Base = \( 4x = 4 \times 8 = 32 \, \text{cm} \)
- Height = \( 5x = 5 \times 8 = 40 \, \text{cm} \)

### Final Answer:
- Base = 32 cm
- Height = 40 cm

Would you like more details or have any questions about the solution?

### Related Questions:
1. What would the base and height be if the ratio was 3:4 instead of 4:5 with the same area?
2. How does the formula for the area of a triangle change if the base or height is doubled?
3. What is the perimeter of the triangle if it’s an equilateral triangle with the same area?
4. If the height were increased by 20%, how would the area change?
5. What is the area of a triangle where the base is 10 cm and the height is 24 cm?

**Tip:** Always ensure that you simplify ratio-based equations carefully, especially when substituting variables.

The base and height of a triangle are in the ratio 4:5. If the area is 640 sq. cm, find the base and height.

Learn how to find the base and height of a triangle given the ratio of 4:5 and the area of 640 sq. cm. This solution involves using the area of a triangle formula and solving a quadratic equation. Suitable for students in Grades 7-9.

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