Question

The area of the triangle 15/32 square centimeters. What is the length of the base? Express your answer as a fraction in simplest form.
3/4 cm

Answer 1

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

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

We know the area is \( \frac{15}{32} \) square centimeters, and the height is \( \frac{3}{4} \) cm. We can rearrange the formula to solve for the base:

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

Substituting the known values:

\[
\text{base} = \frac{2 \times \frac{15}{32}}{\frac{3}{4}}
\]

First, calculate the numerator:

\[
2 \times \frac{15}{32} = \frac{30}{32} = \frac{15}{16} \quad \text{(by simplifying)}
\]

Next, we need to divide by \( \frac{3}{4} \). Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{15}{16} \div \frac{3}{4} = \frac{15}{16} \times \frac{4}{3}
\]

Now calculate the multiplication:

\[
= \frac{15 \times 4}{16 \times 3} = \frac{60}{48}
\]

Now, simplify \( \frac{60}{48} \):

\[
= \frac{60 \div 12}{48 \div 12} = \frac{5}{4}
\]

Thus, the length of the base is:

\[
\boxed{\frac{5}{4}} \text{ cm}
\]