A triangle has an area of 21.15 square inches and a height of 4.7 inches. What is the length of the base?

1. Break Down the Problem

To find the length of the base of the triangle, we will use the formula for the area of a triangle, which is given by: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ In this case, we know the area and the height, and we need to solve for the base.

2. Relevant Concepts

• The formula for the area of a triangle is $A = \frac{1}{2} b h$, where:
  • $A$ is the area,
  • $b$ is the base,
  • $h$ is the height.

3. Analysis and Detail

We can rearrange the area formula to solve for the base: $b = \frac{2A}{h}$ Substituting the known values:

• Area $A = 21.15$ square inches,
• Height $h = 4.7$ inches.

Plugging these values into the equation gives: $b = \frac{2 \times 21.15}{4.7}$

4. Verify and Summarize

Now, let's perform the calculations: $b = \frac{42.3}{4.7} \approx 9$ Thus, the length of the base is approximately 9 inches.

Final Answer

The length of the base of the triangle is approximately $9$ inches.