The area of a triangle is given by the formula A = 1/2bh Solve this for h.
The Correct Answer and Explanation is:
To solve for h in the formula for the area of a triangle:A=12bhA = \frac{1}{2}bhA=21bh
Follow these algebraic steps:
Step-by-step Solution
Step 1: Start with the area formula:A=12bhA = \frac{1}{2}bhA=21bh
Step 2: Multiply both sides of the equation by 2 to eliminate the fraction:2A=bh2A = bh2A=bh
Step 3: Divide both sides of the equation by b to solve for h:h=2Abh = \frac{2A}{b}h=b2A
Final Answer:
h=2Abh = \frac{2A}{b}h=b2A
Textbook-style Explanation
In geometry and algebra, formulas often relate several variables, and you are often required to solve for one variable in terms of the others. The formula for the area of a triangle is:A=12bhA = \frac{1}{2}bhA=21bh
where:
- A is the area of the triangle,
- b is the base of the triangle,
- h is the height.
This formula tells you that the area is equal to one-half times the base times the height. However, sometimes you are given the area and the base, and you are asked to find the height.
To solve the formula for h, begin by isolating h. Start by eliminating the fraction on the right-hand side. You do this by multiplying both sides of the equation by 2:2A=bh2A = bh2A=bh
Now, the right side no longer has the fraction, and the equation is easier to work with. Next, to get h by itself, divide both sides of the equation by b:h=2Abh = \frac{2A}{b}h=b2A
Now, the height h is expressed in terms of the area and the base. This rearranged formula is useful when you know the area and the base and want to find the vertical height of the triangle. It’s especially helpful in practical geometry problems involving measurement or construction. Always remember to include the same units for area and base so that your height will also be in the correct unit.
