The base of a triangle is 2cm less than the altitude and the area of the angle is 60^2 cm. Calculate the altitude
(1/2)(h-2)(h) = 60
Now just solve for h
To calculate the altitude of the triangle, we need to use the formula for the area of a triangle:
Area = (base * altitude) / 2
From the given information, we know that the area is 60^2 cm and the base is 2 cm less than the altitude. Let's set up the equation:
60^2 = (base * altitude) / 2
To simplify the equation, let's call the altitude "x". Since the base is 2 cm less than the altitude, the base can be represented as "x - 2". Now we can substitute these values into the equation:
60^2 = ((x - 2) * x) / 2
To solve for x, we can multiply both sides of the equation by 2:
2 * 60^2 = (x - 2) * x
Now, expand and simplify the equation:
7200 = x^2 - 2x
Rearrange the equation into a quadratic form:
x^2 - 2x - 7200 = 0
Now, we can solve this quadratic equation. Factoring may not be a viable option for this equation, so we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -2, and c = -7200. Plugging these values into the quadratic formula:
x = (-(-2) ± √((-2)^2 - 4(1)(-7200))) / (2 * 1)
Simplifying further:
x = (2 ± √(4 + 28800)) / 2
x = (2 ± √(28804)) / 2
x = (2 ± 169.781) / 2
Now, we have two possible solutions for x:
x1 = (2 + 169.781) / 2 ≈ 170.781 / 2 ≈ 85.39 cm
x2 = (2 - 169.781) / 2 ≈ -167.781 / 2 ≈ -83.89 cm
Since the altitude cannot be negative, the altitude of the triangle is approximately 85.39 cm.