Math Problem Statement
The height of triangle is 4-cm more than twice the length of the base. The area of the triangle is 35 square centimeter. Find the height of the triangle.
Solution
Let's denote the base of the triangle as cm and the height as cm. According to the problem, the height is 4 cm more than twice the base:
The formula for the area of a triangle is given by:
We know the area is 35 square centimeters, so we can substitute the values:
Simplify the equation:
Rearrange the equation into standard quadratic form:
Now, solve this quadratic equation using the quadratic formula:
Let’s plug in the values ().
The solutions for the base are cm and cm. Since the base of a triangle cannot be negative, we take cm.
Now, substitute the value of into the equation for the height:
So, the height of the triangle is 14 cm.
Would you like more details or have any questions? Here are some related questions:
- How would the problem change if the area was different?
- What if the height was a different multiple of the base?
- How can we find the base if the height is known?
- What are other ways to solve this type of problem?
- How does changing the base affect the area?
Tip: When working with geometric problems, always double-check the units and relationships between variables.
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Math Problem Analysis
Mathematical Concepts
Geometry
Algebra
Quadratic Equations
Formulas
Area of a triangle: Area = (1/2) * base * height
Quadratic equation formula: ax^2 + bx + c = 0
Theorems
Quadratic Formula
Area of a Triangle
Suitable Grade Level
Grades 8-10