Answer :

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].