Let's correct the given problem statement first for clarity:
"The area of a triangle is 48 cm². The base is 12 cm. Find the length of its corresponding altitude."
To find the altitude of the triangle, 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:
- Area ([tex]\(A\)[/tex]) = 48 cm²
- Base ([tex]\(b\)[/tex]) = 12 cm
We need to find the height ([tex]\(h\)[/tex]).
Let's start by writing down the area formula:
[tex]\[ 48 = \frac{1}{2} \times 12 \times h \][/tex]
To isolate [tex]\(h\)[/tex], we need to solve for [tex]\(h\)[/tex]:
1. Multiply both sides by 2 to eliminate the fraction:
[tex]\[ 2 \times 48 = 12 \times h \][/tex]
2. Simplify the left side:
[tex]\[ 96 = 12 \times h \][/tex]
3. Now, divide both sides by 12 to solve for [tex]\(h\)[/tex]:
[tex]\[ h = \frac{96}{12} \][/tex]
4. Simplify the division:
[tex]\[ h = 8 \][/tex]
Therefore, the length of the altitude corresponding to the given base of 12 cm is 8 cm.
