Can you PLEASE help me with this problem? I do not understand...
The area of a triangle can be found by using the formula A=1/2bh. The area of the triangle can be represented by the expression
-17.5x2^ - 138.5x - 27. The triangle's base length is greater than its height. If the area of the triangle is 231 square inches, find the value of x as it relates to this rectangle, the numerical length of the base, and the numerical length of the height.
x =
Base =
Height =
You say rectangle. I assume typo? Did you read what you wrote?
All terms in the area are - ?
-17.5 x^2 -138 x - 27 = 231?
+17.5 x +138 x + 258 = 0
x = -3.05 or x = -4.84
231 = -17.5x2^ - 138.5x - 27
462 = -37 x^2 - 277 x - 54
0 = -37 x^2 - 277 x - 516
use quadratic formula to find x
To find the value of x, the length of the base, and the length of the height, we can start by equating the given expression for the area of the triangle to 231 square inches and solving for x.
Given:
Area of the triangle = -17.5x^2 - 138.5x - 27
Area of the triangle = 231 square inches
We can set up the equation:
-17.5x^2 - 138.5x - 27 = 231
Next, we can simplify the equation by adding 231 to both sides:
-17.5x^2 - 138.5x - 27 + 231 = 0
Combining like terms:
-17.5x^2 - 138.5x + 204 = 0
Now, we have a quadratic equation in the form of Ax^2 + Bx + C = 0, where A = -17.5, B = -138.5, and C = 204.
To solve this quadratic equation, we can use the quadratic formula:
x = (-B ± √(B^2 - 4AC)) / (2A)
Plugging in the values:
x = (-(-138.5) ± √((-138.5)^2 - 4(-17.5)(204))) / (2(-17.5))
Simplifying further:
x = (138.5 ± √(19152.25 + 14112)) / (-35)
x = (138.5 ± √(33264.25)) / (-35)
x = (138.5 ± 182.34) / (-35)
This gives us two possible solutions for x:
x1 = (138.5 + 182.34) / (-35) ≈ -10.13
x2 = (138.5 - 182.34) / (-35) ≈ 1.95
Since the length cannot be negative, we can discard the solution x1 = -10.13.
Therefore, the value of x, as it relates to the triangle, is approximately x = 1.95.
To find the lengths of the base and height, we can substitute this value of x into the original expression for the area of the triangle:
Area of the triangle = -17.5x^2 - 138.5x - 27
Area of the triangle = -17.5(1.95)^2 - 138.5(1.95) - 27
Simplifying this expression will give us the base and height lengths of the triangle.