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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. Which shows the equation Brian can use and the correct measure of the height of the triangle?

Respuesta :

the formula for the area of a triangle is 1/2*base*height so setting a=18 you can set up the equation as 18=1/2*b*h which gives 18=1/2*(c-1)*6c. simplifying gives 18=3c(c-1). setting the equation to 0 gives a quadratic which is
3c^2-3c-18=0 which gives c= 3 or -2 since -2 doesnt make sense we can assume c=3 so filling the equation with c=3 gives 18=1/2*(6*3)*(3-1) which gives 18=1/2(18)(2) you see 1/2*2 cancels and you are left with 18=18 which is correct so c=3 and height =18

akposevictor

The equation Brian can use is: 1/2(c - 1)(6c) = 18 or 6c² - 6c - 36 = 0

The height of the triangles is 18 m.

What is the Area of a Triangle?

If h = height of a triangle, and b is the base of the triangle, then the area of a triangle is expressed as: 1/2(b)(h).

Given:

h = 6c m

b = (c - 1) m

Area of triangle = 18 sq. m

The equation that Brian can use would be:

1/2(c - 1)(6c) = 18

Find the value of c:

(c - 1)(6c) = 36

6c² - 6c = 36

6c² - 6c - 36 = 0

Factoring and setting each factor equal to zero, we will have:

c = 3, or c = -2

Lets use the positive value of c. Thus:

height of the triangle = 6c

Substitute c = 3

height of the triangle = 6(3) = 18 m.

Thus, the equation Brian can use is: 1/2(c - 1)(6c) = 18 or 6c² - 6c - 36 = 0

The height of the triangles is 18 m.

Learn more about the area of triangle on:

https://brainly.com/question/21735282

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