Simone used this formula to find the height of a triangle:
[tex]$a=\frac{1}{2} b h$[/tex]
She knew the area, [tex]$a$[/tex], and [tex]$b$[/tex], the base of the triangle. How can she rearrange the formula to isolate [tex]$h$[/tex] to find the height, [tex]$h$[/tex]?
A. divide both sides by 2, divide by [tex]$h$[/tex]
B. divide both sides by 2, multiply by [tex]$h$[/tex]
C. multiply both sides by 2, multiply by [tex]$b$[/tex]
D. multiply both sides by 2, divide by [tex]$b$[/tex]
Answer (2)
Multiply both sides of the equation a = 2 1 bh by 2 to get 2 a = bh .
Divide both sides of the equation 2 a = bh by b to isolate h .
The rearranged formula is h = b 2 a .
Therefore, the correct answer is to multiply both sides by 2 and divide by b .
Explanation
Understanding the Formula We are given the formula for the area of a triangle: a = 2 1 bh , where a is the area, b is the base, and h is the height. We want to isolate h to find the height of the triangle.
Multiplying by 2 To isolate h , we need to get rid of the 2 1 and b that are multiplied with h . First, let's multiply both sides of the equation by 2 to get rid of the fraction: 2 × a = 2 × 2 1 bh 2 a = bh
Dividing by b Now, we need to get rid of the b that is multiplied with h . To do this, we divide both sides of the equation by b :
b 2 a = b bh b 2 a = h
Final Answer So, we have h = b 2 a . This means we multiplied both sides of the original equation by 2 and then divided both sides by b to isolate h .
Examples
Understanding how to rearrange formulas is crucial in many real-world applications. For example, if you're designing a triangular sail for a boat and you know the desired area of the sail and the length of the base, you can use the rearranged formula to calculate the required height of the sail. Similarly, in construction, if you're building a triangular support structure and you know the area and base length, you can determine the necessary height for the structure. This skill is also useful in fields like architecture and engineering, where geometric calculations are essential for design and planning.
To isolate the height h of the triangle from the area formula a = 2 1 bh , multiply both sides by 2 to get 2 a = bh , then divide by b to find h = b 2 a . The correct answer is option D: multiply both sides by 2, divide by b .
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