A triangular lot in a park has a base with a measure that is 4 more than twice the height of the lot. The area of the lot is 99 square feet. Since the area of a triangle is found by using the formula A= 1/2bh, the area for this lot can be represented by the equation 99=1/2(2h+4)h, where h represents the height of the triangle.
What is the height of the lot?
Once again, I am not sure what the steps are for figuring out this problem. Someone please give me the steps for solving this problem PLEASE!! thank you
solve the given equation for h
rearranging and simplifying ... 0 = h^2 + 2 h - 99
factor or use the quadratic formula
99 = 1/2(2h+4)h.
99 = (h+2)h,
99 = h^2 + 2h,
h^2 + 2h - 99 = 0. Solve for h:
h = (-B +- Sqrt(B^2-4AC))/2A.
h = (-2 +- Sqrt(4 + 396))/2,
h = (-2 +- 20)/2 = -1 +- 10 = 9, and -11 Ft.
Use the positive number: h = 9 Ft.
To solve this problem, we need to rearrange the equation and solve for the height (h).
Step 1: Simplify the equation.
Start by expanding the expression on the right-hand side of the equation:
99 = (1/2)(2h + 4)h
Multiply the terms inside the parentheses:
99 = (1/2)(2h^2 + 4h)
Distribute the 1/2 to each term inside the parentheses:
99 = h^2 + 2h
Step 2: Rearrange the equation.
Rearrange the equation to get the quadratic equation in standard form (ax^2 + bx + c = 0):
h^2 + 2h - 99 = 0
Step 3: Solve the quadratic equation.
Now we can solve the quadratic equation using factoring, completing the square, or the quadratic formula. Let's use factoring in this case.
We need to find two numbers whose product is -99 (the constant term) and whose sum is 2 (the coefficient of the linear term). The numbers are 11 and -9.
Thus, we rewrite the equation as:
(h + 11)(h - 9) = 0
Setting each factor equal to zero gives us two solutions:
h + 11 = 0 or h - 9 = 0
Solving for h in each equation:
h = -11 or h = 9
Step 4: Determine the appropriate solution.
In this problem, since we are dealing with the physical height of a lot, the height cannot be negative. Therefore, we discard the solution h = -11.
Thus, the height of the lot is h = 9 feet.
In summary, the height of the lot is 9 feet.