To find the height of the triangle given its area, we can use the formula for the area of a triangle:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
Given:
- The area of the triangle is [tex]\( 126 \, \text{ft}^2 \)[/tex].
- The base of the triangle is [tex]\( 14 \, \text{ft} \)[/tex].
We need to find the height of the triangle.
Step-by-step solution:
1. Substitute the given values for the area and the base into the area formula:
[tex]\[ 126 = \frac{1}{2} \times 14 \times \text{height} \][/tex]
2. To isolate the height, first clear the fraction by multiplying both sides of the equation by 2:
[tex]\[ 2 \times 126 = 14 \times \text{height} \][/tex]
[tex]\[ 252 = 14 \times \text{height} \][/tex]
3. Now, solve for the height by dividing both sides of the equation by the base (14):
[tex]\[ \frac{252}{14} = \text{height} \][/tex]
[tex]\[ 18 = \text{height} \][/tex]
Therefore, the height of the triangle is [tex]\( 18 \, \text{ft} \)[/tex].
