Question

The area of the triangle below is 2/15 ft
​
square feet. What is the length of the base? Express your answer as a fraction in simplest form.
2/5 ft

Answer 1

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

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

In this case, we know the area is \( \frac{2}{15} \) square feet and the height (which we'll denote as \( h \)) is \( \frac{2}{5} \) feet. We can rearrange the formula to solve for the base:

\[
\frac{2}{15} = \frac{1}{2} \times \text{base} \times \frac{2}{5}
\]

Now we multiply both sides of the equation by 2 to eliminate the fraction:

\[
\frac{4}{15} = \text{base} \times \frac{2}{5}
\]

Next, we can solve for the base by multiplying both sides by the reciprocal of \( \frac{2}{5} \):

\[
\text{base} = \frac{4}{15} \times \frac{5}{2}
\]

Now we perform the multiplication:

\[
\text{base} = \frac{4 \times 5}{15 \times 2} = \frac{20}{30}
\]

Now we simplify \( \frac{20}{30} \):

\[
\frac{20}{30} = \frac{2}{3}
\]

Thus, the length of the base is

\[
\boxed{\frac{2}{3}} \text{ ft}
\]