What is the height of a triangle whose base is 10 cm and whose area is 75 cm²?
Understand the Problem
The question asks to find the height of a triangle when the base and area are known. We can use the formula for the area of a triangle (Area = 1/2 * base * height) to solve for the height.
Answer
b. 15 cm
Answer for screen readers
b. 15 cm
Steps to Solve
- Write down the formula for the area of a triangle
The area of a triangle is given by:
$$Area = \frac{1}{2} \times base \times height$$
- Plug in the given values
We are given that the area is $75 \text{ cm}^2$ and the base is $10 \text{ cm}$. Let $h$ be the height. So, we have:
$$75 = \frac{1}{2} \times 10 \times h$$
- Simplify the equation
$$75 = 5h$$
- Solve for $h$
Divide both sides of the equation by 5:
$$h = \frac{75}{5} = 15$$
So, the height of the triangle is $15 \text{ cm}$.
b. 15 cm
More Information
The height of the triangle is 15 cm.
Tips
A common mistake is to forget the $1/2$ factor in the area of a triangle formula. Another common mistake is incorrectly rearranging the equation when solving for the height.
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