Math Problem Statement

The area A of a triangle is represented by the formula A = 1/2 * b * h where b is the base and h is the height. Write an equation that makes it easy to find the base if we know the area and the height.

Solution

The problem states:

The area AA of a triangle is represented by the formula:

A=12bhA = \frac{1}{2} b h

where bb is the base and hh is the height. The task is to rewrite this formula in a way that makes it easy to find the base bb if we know the area AA and the height hh.

To isolate bb, we can rearrange the formula as follows:

  1. Start with the formula for the area of a triangle: A=12bhA = \frac{1}{2} b h

  2. Multiply both sides by 2 to eliminate the fraction: 2A=bh2A = b h

  3. Divide both sides by hh to solve for bb: b=2Ahb = \frac{2A}{h}

So, the equation that makes it easy to find the base bb given the area AA and height hh is:

b=2Ahb = \frac{2A}{h}

Would you like a further breakdown of the solution steps or have any other questions?

Here are some related questions you might find useful:

  1. How do you rearrange a formula to isolate a variable?
  2. How does changing the height hh affect the base bb if the area is constant?
  3. What happens to the value of bb if both AA and hh double?
  4. How can we use this formula to check if a given triangle has the correct dimensions for a specific area?
  5. How does this formula relate to the area of other shapes?

Tip: When rearranging equations, always perform the same operation on both sides to maintain equality.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry

Formulas

Area of a triangle A = 1/2 * b * h

Theorems

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Suitable Grade Level

Grades 6-8