Question
The composite figure has an area of 156 square meters. What is the height of the triangle? The base of the triangle is 12m
(1 point)
Responses
7 meters
7 meters
8 meters
8 meters
3 meters
3 meters
6 meters
(1 point)
Responses
7 meters
7 meters
8 meters
8 meters
3 meters
3 meters
6 meters
Answers
Answered by
GPT-4o mini
To find the height of a triangle given the area and the base, we can use the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
You stated that the area of the triangle is 156 square meters and the base is 12 meters. We can rearrange the formula to solve for the height:
\[
\text{height} = \frac{2 \times \text{Area}}{\text{base}}
\]
Substituting in the known values:
\[
\text{height} = \frac{2 \times 156}{12}
\]
Simplifying this:
\[
\text{height} = \frac{312}{12} = 26
\]
Since 26 meters is not one of the response options provided, and it seems that this context did not ask for more triangles or figures, there appears to be a mismatch with the responses or perhaps the area originally stated was meant for another figure or composite shape.
Nonetheless, if we are strictly looking for a height based on the area and base provided for a triangle, 26 meters would be the calculated height based on the provided area of the triangle. Please double-check whether the area or base belongs to another part of the composite figure.
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
You stated that the area of the triangle is 156 square meters and the base is 12 meters. We can rearrange the formula to solve for the height:
\[
\text{height} = \frac{2 \times \text{Area}}{\text{base}}
\]
Substituting in the known values:
\[
\text{height} = \frac{2 \times 156}{12}
\]
Simplifying this:
\[
\text{height} = \frac{312}{12} = 26
\]
Since 26 meters is not one of the response options provided, and it seems that this context did not ask for more triangles or figures, there appears to be a mismatch with the responses or perhaps the area originally stated was meant for another figure or composite shape.
Nonetheless, if we are strictly looking for a height based on the area and base provided for a triangle, 26 meters would be the calculated height based on the provided area of the triangle. Please double-check whether the area or base belongs to another part of the composite figure.
Answer
The answer is 6 meters