To find the height of a triangle given its area and base, we can use the formula for the area of a triangle:
[tex]\[
A = \frac{1}{2} b h
\][/tex]
Here, [tex]\(A\)[/tex] is the area of the triangle, [tex]\(b\)[/tex] is the base, and [tex]\(h\)[/tex] is the height. We need to solve for the height [tex]\(h\)[/tex].
Given:
- The area [tex]\(A\)[/tex] is 35 square inches.
- The base [tex]\(b\)[/tex] is 7 inches.
Step-by-step, we need to rearrange the formula to solve for the height [tex]\(h\)[/tex]:
1. Start with the area formula:
[tex]\[
A = \frac{1}{2} b h
\][/tex]
2. Substitute the known values of [tex]\(A\)[/tex] and [tex]\(b\)[/tex] into the formula:
[tex]\[
35 = \frac{1}{2} \times 7 \times h
\][/tex]
3. Simplify the equation by multiplying:
[tex]\[
35 = \frac{7}{2} \times h
\][/tex]
4. To isolate [tex]\(h\)[/tex], multiply both sides of the equation by 2 to get rid of the fraction:
[tex]\[
2 \times 35 = 7 \times h
\][/tex]
5. This simplifies to:
[tex]\[
70 = 7 \times h
\][/tex]
6. Finally, solve for [tex]\(h\)[/tex] by dividing both sides of the equation by 7:
[tex]\[
h = \frac{70}{7}
\][/tex]
7. Perform the division:
[tex]\[
h = 10
\][/tex]
Therefore, the height of the triangle is [tex]\(10\)[/tex] inches.
So, the correct answer is:
[tex]\[
10 \text{ inches}
\][/tex]
