Answer:
[tex]5B^{2} - 12B +10B - 24 = 0\\\\\[/tex] Base of triangle = 2.4 Feet and Height of triangle = 10 feet.
Step-by-step explanation:
This problem can be solved by using formula to calculate area of triangle.
Area of triangle = 1/2*(base*height)
given
Let base of triangle B
height if triangle H
according to problem
The height of a triangle is 2 less than 5 times its base
mathematically it can be expressed as
H = 5*B - 2
Given area of triangle= 12 sq feet
Area of triangle = 1/2*(base*height)
=> 12 = 1/2* {B*(5*B-2)}
=> 24 = 5B^2 - 2B
[tex]5B^{2} - 12B +10B - 24 = 0\\\\\[/tex] which is a quadratic equation
It can be solved as given below
[tex]5B^{2} +10B - 12B - 24 = 0\\\\\=>5B(B +2) -12(B +2) = 0\\=> (5B - 12) (B +2) = 0\\5B - 12 = 0 or B + 2 = 0\\Hence B = 12/5 \ or \ B = -2\\\\[/tex]
Since for side of triangle B cannot be negative number hence B= 12/5 = 2.4
Therefore height of triangle = 5*B - 2 = 5*2.4 - 2 = 12 - 2 = 10
Base of triangle = 2.4 Feet and Height of triangle = 10 feet.
Equation which models this situation is
[tex]5B^{2} - 12B +10B - 24 = 0\\\\\[/tex]
