Answer:
height = 12 cm
base length = 4 cm
Step-by-step explanation:
area of a triangle
base length × height / 2
x = height
y = base length
x = y + 8
24 = y × (y + 8) / 2
48 = y × (y + 8) = y² + 8y
squared equation
y² + 8y - 48 = 0
solution
y = (-b ± sqrt(b² - 4ac))/(2a)
a = 1
b = 8
c = -48
y = (-8 ± sqrt(64 - 4×-48))/2 = (-8 ± sqrt(64 + 192))/2 =
= (-8 ± sqrt(256))/2 = (-8 ± 16)/2 = -4 ± 8
y1 = -4 + 8 = 4 cm
y2 = -4 - 8 = -12
but a negative base length did not make any sense, so only y = 4 remains.
x = y + 8 = 4 + 8 = 12 cm
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Answer:
y = -2/5x +36/5 . . . . . slope-intercept form
2x +5y = 36 . . . . . . . . standard form
Step-by-step explanation:
You can use the 2-point form of the equation of a line to find it.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (4 -6)/(8 -3)(x -3) +6
y = -2/5(x -3) +6
y = -2/5x +36/5 . . . . slope-intercept form
2x +5y = 36 . . . . . . . standard form
6xy^2 - xy + 8 + 12y is a polynomial of degree 3
