Question
The area of the triangle below is 1/16 square centimeters. What is the length of the base? Express your answer as a fraction in simplest form
Answers
GPT-4o mini
To determine the length of the base of a triangle given its area, we use the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this problem, we know the area of the triangle is \( \frac{1}{16} \) square centimeters. We can denote the length of the base as \( b \) and the height as \( h \). Therefore, we can rewrite the area formula as:
\[
\frac{1}{16} = \frac{1}{2} \times b \times h
\]
To solve for \( b \), we first multiply both sides of the equation by 2 to eliminate the fraction:
\[
\frac{1}{8} = b \times h
\]
Now, we can isolate \( b \):
\[
b = \frac{1}{8h}
\]
At this point, we need the height \( h \) to calculate \( b \). If the height is not provided, we could express \( b \) in terms of \( h \). However, without specific information regarding the height, we can't find a unique value for \( b \).
If we express it in terms of \( h \):
- When \( h = 1 \), \( b = \frac{1}{8} \).
- When \( h = 2 \), \( b = \frac{1}{16} \).
And so on.
In conclusion, without a specific height given, the length of the base \( b \) can be expressed in terms of the height \( h \):
\[
b = \frac{1}{8h}
\]
To ensure a unique answer, we would need to know the height of the triangle. If a specific height is given, we can substitute it into this formula to find \( b \).
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this problem, we know the area of the triangle is \( \frac{1}{16} \) square centimeters. We can denote the length of the base as \( b \) and the height as \( h \). Therefore, we can rewrite the area formula as:
\[
\frac{1}{16} = \frac{1}{2} \times b \times h
\]
To solve for \( b \), we first multiply both sides of the equation by 2 to eliminate the fraction:
\[
\frac{1}{8} = b \times h
\]
Now, we can isolate \( b \):
\[
b = \frac{1}{8h}
\]
At this point, we need the height \( h \) to calculate \( b \). If the height is not provided, we could express \( b \) in terms of \( h \). However, without specific information regarding the height, we can't find a unique value for \( b \).
If we express it in terms of \( h \):
- When \( h = 1 \), \( b = \frac{1}{8} \).
- When \( h = 2 \), \( b = \frac{1}{16} \).
And so on.
In conclusion, without a specific height given, the length of the base \( b \) can be expressed in terms of the height \( h \):
\[
b = \frac{1}{8h}
\]
To ensure a unique answer, we would need to know the height of the triangle. If a specific height is given, we can substitute it into this formula to find \( b \).