The formula for the area of a triangle is [tex]$A=\frac{1}{2} b h$[/tex], where [tex]$b$[/tex] is the length of the base and [tex]$h$[/tex] is the height. Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.
Answer (2)
Substitute the given area and base into the triangle area formula.
Simplify the equation to isolate the height.
Divide both sides by 6 to solve for the height.
The height of the triangle is 5 units.
Explanation
Problem Setup and Given Information 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 are given that the area A = 30 square units and the base b = 12 units. We need to find the height h .
Substitute Values Substitute the given values into the formula: 30 = 2 1 ( 12 ) h
Simplify Simplify the equation: 30 = 6 h
Solve for h To solve for h , divide both sides of the equation by 6: 6 30 = 6 6 h 5 = h
Final Answer Therefore, the height of the triangle is 5 units.
Examples
Understanding how to calculate the height of a triangle given its area and base is useful in many real-world scenarios. For example, architects and engineers use this principle when designing structures with triangular elements, such as roof trusses or bridge supports. Knowing the area and base allows them to determine the necessary height to ensure structural integrity and aesthetic appeal. Similarly, landscapers might use this to calculate the dimensions of triangular flower beds or garden features, ensuring they fit within the available space and provide the desired visual impact. This simple formula is a fundamental tool in various design and construction applications.
The height of the triangle is found to be 5 units using the area formula. By substituting the known area and base into the formula and simplifying, we determined the height. This is achieved through algebraic manipulation to isolate the height variable.
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