The base of a triangle is 1 cm more than 3 times its height. If the area of the triangle is 15 cm^2. Determine the length of the base and the height of this triangle.
I just did this for you a minute or two ago. Read your first post before doing it again!
The vertex of the quadratic function y = 2x^2+8x + c is (x, 3) .
On Blank 1, state the value of x-coordinate of the vertex
On Blank 2, state the value of m
the vertex is at x = -b/2a
so, x = -8/4 = -2
I have no idea what m is, but the above answer means that c=11
check
y = 2x^2+8x+c
= 2(x^2+4x) + c
= 2(x^2+4x+4) + c-2*4
= 2(x+2)^2 + c-8
so
3 = c-8
c = 11
To determine the length of the base and the height of the triangle, we can start by setting up an equation based on the given information.
Let's assume that the height of the triangle is 'h' cm. According to the problem statement, the base of the triangle is 1 cm more than 3 times its height, which can be expressed as (3h + 1) cm.
The formula to calculate the area of a triangle is:
Area = (1/2) * base * height
Plugging in the given values, we can now write the equation as follows:
15 cm^2 = (1/2) * (3h + 1) * h
To simplify the equation, let's eliminate the fraction by multiplying both sides by 2:
30 cm^2 = (3h + 1) * h
Now, let's expand and rearrange the equation:
30 cm^2 = 3h^2 + h
Rearranging the equation gives us a quadratic equation:
3h^2 + h - 30 = 0
To solve this quadratic equation, we can factorize or use the quadratic formula. In this case, let's use the quadratic formula:
The quadratic formula is:
h = (-b ± √(b^2 - 4ac)) / 2a
For this equation, a = 3, b = 1, and c = -30.
h = (-(1) ± √((1)^2 - 4(3)(-30))) / (2(3))
h = (-1 ± √(1 + 360)) / 6
h = (-1 ± √361) / 6
Now, we can simplify further:
h = (-1 ± 19) / 6
So, we have two possible values for the height:
h1 = (-1 + 19) / 6 = 18 / 6 = 3 cm
h2 = (-1 - 19) / 6 = -20 / 6 = -10 / 3 ≈ -3.333 cm
Since the height of a triangle cannot be negative, we discard the negative value of -3.333 cm.
Therefore, the height of the triangle is 3 cm.
To find the length of the base, we substitute the value of h back into the expression for the base:
base = 3h + 1
base = 3(3) + 1
base = 9 + 1
base = 10 cm
So, the length of the base of the triangle is 10 cm, and the height of the triangle is 3 cm.