To find the height of the triangle with a given area of [tex]\(126 \text{ ft}^2\)[/tex], 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 that the area ([tex]\(A\)[/tex]) is 126 square feet, and assuming a base ([tex]\(b\)[/tex]) of 14 feet, we can set up the equation as follows:
[tex]\[
126 = \frac{1}{2} \times 14 \times \text{height}
\][/tex]
First, solve for the height by isolating it on one side of the equation. Multiply both sides by 2 to remove the fraction:
[tex]\[
2 \times 126 = 14 \times \text{height}
\][/tex]
This simplifies to:
[tex]\[
252 = 14 \times \text{height}
\][/tex]
Now, divide both sides of the equation by 14 to solve for the height:
[tex]\[
\text{height} = \frac{252}{14}
\][/tex]
This simplifies to:
[tex]\[
\text{height} = 18 \text{ ft}
\][/tex]
Thus, the height of the triangle is [tex]\(18 \text{ feet}\)[/tex].
