Question

The area of the triangle below is 1/48.what is the length of the base? express your fraction in simplest form. The height is 1/6

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The area \(A\) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Given that the area \(A = \frac{1}{48}\) and the height \(h = \frac{1}{6}\) , we can substitute these values into the formula and solve for the base:
\[ \frac{1}{48} = \frac{1}{2} \times \text{base} \times \frac{1}{6} \]
First, multiply both sides by \(2\) to get rid of the \(\frac{1}{2}\) fraction:
\[ \frac{1}{48} \times 2 = \text{base} \times \frac{1}{6} \]
\[ \frac{2}{48} = \frac{\text{base}}{6} \]
\[ \frac{1}{24} = \frac{\text{base}}{6} \]
Now, multiply both sides by \(6\) to solve for the base:
\[ \frac{1}{24} \times 6 = \text{base} \]
\[ \frac{1}{4} = \text{base} \]
So, the length of the base is \(\frac{1}{4}\) .

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