A = 1/2bh, solve for b. Can someone show me the steps to solve this?
The Correct Answer and Explanation is:
To solve the formula A = ½bh for b, follow these algebraic steps:
Step-by-Step Solution:
Given:
A = ½ × b × h
We want to solve for b (make b the subject of the formula).
Step 1: Eliminate the fraction.
Multiply both sides of the equation by 2 to eliminate the ½: 2A=bh2A = bh2A=bh
Step 2: Solve for b.
To isolate b, divide both sides of the equation by h: 2Ah=b\frac{2A}{h} = bh2A=b
Final Answer: b=2Ahb = \frac{2A}{h}b=h2A
Textbook-Style Explanation (Approx. 300 Words)
In algebra, solving for a variable means rearranging an equation to isolate that variable on one side of the equation. Here, we are given the formula for the area A of a triangle: A=12bhA = \frac{1}{2}bhA=21bh
This formula tells us that the area of a triangle is equal to one-half the product of its base (b) and its height (h). The goal is to solve for b, which means expressing b in terms of A and h.
The first step is to eliminate the fraction, since working with whole numbers is often easier. We do this by multiplying both sides of the equation by 2: 2A=bh2A = bh2A=bh
Now that we’ve eliminated the fraction, we can focus on isolating the variable b. Notice that b is being multiplied by h. To undo multiplication, we use the opposite operation—division. So we divide both sides of the equation by h: 2Ah=b\frac{2A}{h} = bh2A=b
This gives us the final expression for b: b=2Ahb = \frac{2A}{h}b=h2A
This new formula is useful when you know the area and height of a triangle and need to find the length of the base. By rearranging the original formula, we have made b the subject, and the expression on the right-hand side now shows how to calculate b directly. This technique is essential in algebra and is widely used in physics, engineering, and geometry.
