To find the height of a triangle given its area and base, we can use the formula for the area of a triangle, which is:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
Given:
- The area of the triangle is 15 square inches.
- The base of the triangle is 5 inches.
We need to find the height. Let's denote the height by [tex]\( h \)[/tex].
First, rewrite the formula to solve for [tex]\( h \)[/tex]:
[tex]\[ 15 = \frac{1}{2} \times 5 \times h \][/tex]
Next, simplify the equation:
[tex]\[ 15 = \frac{1}{2} \times 5 \times h \][/tex]
[tex]\[ 15 = \frac{5}{2} \times h \][/tex]
To isolate [tex]\( h \)[/tex], multiply both sides of the equation by 2:
[tex]\[ 2 \times 15 = 5 \times h \][/tex]
[tex]\[ 30 = 5 \times h \][/tex]
Now, divide both sides by 5 to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{30}{5} \][/tex]
[tex]\[ h = 6 \][/tex]
Therefore, the height of the triangle is 6 inches.
