5. 
Find the height of a triangle with an area (A) of 35 square inches and base (b) of 7 inches. Use the formula for the area of a triangle, A=1/2 bh.


2.5 inches


122.5 inches


10 inches


490 inches

To find the height of a triangle when given the area and the base, we use the formula for the area of a triangle:
\[
A = \frac{1}{2} b h
\]
where \( A \) is the area, \( b \) is the base, and \( h \) is the height.

Given:
\[
A = 35 \text{ square inches}
\]
\[
b = 7 \text{ inches}
\]

We need to find \( h \).

1. Substitute the given values into the formula:
   \[
   35 = \frac{1}{2} \cdot 7 \cdot h
   \]

2. Simplify the equation:
   \[
   35 = \frac{7}{2} \cdot h
   \]

3. Multiply both sides by 2 to get rid of the fraction:
   \[
   2 \cdot 35 = 7 \cdot h
   \]

4. Simplify:
   \[
   70 = 7h
   \]

5. Divide both sides by 7 to solve for \( h \):
   \[
   h = \frac{70}{7} = 10
   \]

So, the height of the triangle is:
\[
h = 10 \text{ inches}
\]

The correct answer is: 10 inches.

Do you want more details or have any questions?

Here are 8 related questions for further practice:

1. Find the height of a triangle with an area of 50 square inches and a base of 10 inches.
2. If the base of a triangle is 14 inches and the height is 5 inches, what is the area of the triangle?
3. A triangle has an area of 21 square inches and a height of 7 inches. What is the length of its base?
4. Find the base of a triangle with an area of 48 square inches and a height of 6 inches.
5. What is the area of a triangle with a base of 8 inches and a height of 12 inches?
6. A triangle has a base of 5 inches and a height of 4 inches. What is its area?
7. If a triangle has an area of 28 square inches and a base of 4 inches, what is its height?
8. Calculate the height of a triangle with an area of 84 square inches and a base of 14 inches.

**Tip:** Always double-check your units when solving geometry problems to ensure consistency and correctness.

Learn how to find the height of a triangle when given the area and base dimensions. This problem involves applying the formula for the area of a triangle, A = 1/2 * base * height. Suitable for students in Grades 6-8.

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