Final answer:
To find the base and height of a triangle with an area of 75 square units, first express the base as 5 units less than twice the height. Solve for height using the area formula and linear equation, then determine the base using the height value.
Step-by-step explanation:
To find the base and height of the triangle when given the area and a relationship between the base and height, we can use the formula for the area of a triangle, which is Area = 1/2 × base × height. We are told the base of the triangle is 5 units less than twice the height, which can be expressed as base = 2×height - 5. Since the area of the triangle is 75 square units, the formula becomes 75 = 1/2 × (2×height - 5) × height.
Now we solve this equation for height:
- 150 = (2×height - 5) × height
- 150 = 2×height^2 - 5×height
- 0 = 2×height^2 - 5×height - 150
This quadratic equation can be solved by factoring, using the quadratic formula, or by graphing the equation and finding the roots.
Once the height is found, it can be substituted back into the formula base = 2×height - 5 to find the base. Remember to verify the result by ensuring that the area calculated with the derived base and height equals the given area of 75 square units.