The area of the triangle below is start fraction, 10, divided by, 9, end fraction 
9
10
​
  square feet. What is the length of the base? Express your answer as a fraction in simplest form.
4/3 ft
Answer

b, equalsb=
ft ft

The area of a triangle is given by the formula:

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

We are told that the area of the triangle is \( \frac{10}{9} \) square feet. Let's assume the base of the triangle is \( b \) feet and the height is \( h = \frac{4}{3} \) feet, as given in the problem.

Using the area formula:

\[
\frac{1}{2} \times b \times \frac{4}{3} = \frac{10}{9}
\]

Now, solve for \( b \):

\[
b \times \frac{4}{3} = 2 \times \frac{10}{9}
\]

\[
b \times \frac{4}{3} = \frac{20}{9}
\]

Multiply both sides by the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):

\[
b = \frac{20}{9} \times \frac{3}{4}
\]

Simplifying:

\[
b = \frac{60}{36} = \frac{5}{3}
\]

Thus, the length of the base \( b \) is \( \frac{5}{3} \) feet.

---

Would you like more details on any step of the process or have any questions? 

Here are some related questions:
1. How would the solution change if the height were different?
2. What happens to the area of a triangle if both the base and height are doubled?
3. How do you find the area of a triangle when you only know the three sides?
4. How would you express the area of this triangle as a decimal instead of a fraction?
5. How can you verify that the fraction \( \frac{5}{3} \) is in its simplest form?

**Tip:** Always cross-check units (like feet, meters) when solving geometry problems to avoid confusion!

The area of the triangle below is 10/9 square feet. What is the length of the base? Express your answer as a fraction in simplest form. Height is 4/3 ft.

Learn how to find the base of a triangle when the area is 10/9 square feet and the height is 4/3 feet. This problem involves geometry and fraction multiplication. The solution uses the area of a triangle formula, suitable for students in Grades 6-8.

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