To find the length of the base of the triangle, we can use the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Given:

• Area = 34 square inches
• Height = $8 \frac{1}{2}$ inches, or 8.5 inches
• Base = $b$ (unknown)

Substitute the given values into the area formula:

$34 = \frac{1}{2} \times b \times 8.5$

To solve for $b$, first multiply both sides by 2 to eliminate the fraction:

$68 = b \times 8.5$

Next, divide both sides by 8.5:

$b = \frac{68}{8.5} = 8$

Thus, the length of the base of the triangle is 8 inches.

---

Would you like further details or clarification?

Here are 5 related questions:

1. How do you calculate the area of a triangle when given the base and height?
2. What would happen to the area if the base was doubled but the height stayed the same?
3. How do you find the height of a triangle when the base and area are known?
4. Can you apply the same method for non-right-angled triangles?
5. What happens if you know the area and base but not the height?

Tip: Always double-check that you're using consistent units when calculating area!