To find the height of a triangle given its area and base, we can use the formula for the area of a triangle:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
We are given:
- The area of the triangle is [tex]\( 15 \)[/tex] square inches.
- The base of the triangle is [tex]\( 5 \)[/tex] inches.
Let's denote the height of the triangle as [tex]\( h \)[/tex]. Plugging the known values into the formula, we have:
[tex]\[ 15 = \frac{1}{2} \times 5 \times h \][/tex]
First, simplify the right-hand side:
[tex]\[ 15 = \frac{5}{2} \times h \][/tex]
To solve for [tex]\( h \)[/tex], we can multiply both sides of the equation by [tex]\( 2 \)[/tex]:
[tex]\[ 2 \times 15 = 5 \times h \][/tex]
[tex]\[ 30 = 5 \times h \][/tex]
Next, divide both sides by [tex]\( 5 \)[/tex]:
[tex]\[ h = \frac{30}{5} \][/tex]
[tex]\[ h = 6 \][/tex]
So, the height of the triangle is [tex]\( 6 \)[/tex] inches.
Now, let's match this result with the provided answer choices:
A) 12
B) [tex]\( 37 \frac{1}{2} \)[/tex]
C) [tex]\( \frac{3}{2} \)[/tex]
D) 3
E) None of these
Since 6 inches is not listed as one of the options (A through D), the correct answer is:
E) None of these
