The equation Brian can use is [0.5(c – 1)(6c) = 18] and the height of the triangle is 18 m and this can be determined by forming the quadratic equation.
Given :
- A triangle’s height is 6c meters and the base is (c – 1) meters.
- Brian knows that the area of the triangle is 18 square meters and is trying to find the height.
The formula of the area of the triangle is given by:
[tex]\rm A = \dfrac{1}{2}BH[/tex]
where A is the area of the triangle, B is the base of the triangle, and H is the height of the triangle.
Now, substitute the values of A, B, and H in the above formula of the area of the triangle.
[tex]\rm 18 = \dfrac{1}{2} \times (c - 1)\times 6c[/tex]
Simplify the above expression in order to determine the value of 'c'.
[tex]36 = 6c(c-1)[/tex]
[tex]\rm 6c^2-6c = 36[/tex]
[tex]c^2 - c - 6= 0[/tex]
Factorize the above equation.
[tex]c^2 -3c + 2c -6=0[/tex]
c(c - 3) + 2(c - 3) = 0
(c - 3)(c + 2) = 0
c = 3 or -2
c never be negative so, the value of c is 3.
The height of the triangle is given by:
= 6(3)
= 18 m
For more information, refer to the link given below:
https://brainly.com/question/19305981
