Atriangle has a base that is twice its height minus 4 feet. if the area is 15 square feet, find the height and base of the triangle.
h = x feet. B = 2X - 4.
A = Bh/2 = (2X -4)X/2 = 15.
Cross multiply:
2X^2 -4X = 30, X^2 -2X -15 = 0,
Solve for X BY FACTORING:
(X -5) (X + 3) = 0
X - 5 = 0, X = 5; X + 3 = 0, X = -3
Choose positive value: X = 5 = height.
2X -4 = 10 -4 = 6 = Base.
ihave a triangle with an area of 35 solve for base and height if height is 3meters less than the base
To find the height and base of the triangle, we can use the formula for the area of a triangle. The formula for the area of a triangle is given by:
Area = (1/2) * base * height
In this case, we are given that the area is 15 square feet. So we can plug this value into the formula:
15 = (1/2) * base * height
Now let's use the given information: the base is twice the height minus 4 feet. We can express this as:
base = 2*height - 4
Substituting this value for the base in our formula, we get:
15 = (1/2) * (2*height - 4) * height
Now we can simplify and solve for the height. Let's multiply both sides by 2 to get rid of the fraction:
30 = (2*height - 4) * height
Expanding the equation, we get:
30 = 2*height^2 - 4*height
Rearranging the equation, we have:
2*height^2 - 4*height - 30 = 0
This is a quadratic equation. We can solve it by factoring or using the quadratic formula. In this case, let's solve it using the quadratic formula:
height = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 2, b = -4, and c = -30. Substituting these values into the formula, we get:
height = (-(-4) ± √((-4)^2 - 4*2*(-30))) / (2*2)
Simplifying further, we have:
height = (4 ± √(16 + 240)) / 4
height = (4 ± √256) / 4
height = (4 ± 16) / 4
height = (4 + 16) / 4 or height = (4 - 16) / 4
height = 20/4 or height = -12/4
height = 5 or height = -3
Since the height of the triangle cannot be negative, we discard the negative solution. Therefore, the height of the triangle is 5 feet.
To find the base, we can substitute the height into the equation for the base:
base = 2*height - 4
base = 2*5 - 4
base = 10 -4
base = 6 feet
Therefore, the height of the triangle is 5 feet and the base is 6 feet.