Question

a triangles 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? area of a triangle = 0.5(base)(height) 0.5(c - 1)(6c)=18; height = 3 meters 0.5(c - 1)(6c)=18; height = 18 meters (c - 1)(6c)=18; height = 3 meters (c - 1)(6c)=18; height = 18 meters

Explanation:

Step1: Apply area formula

The area formula of a triangle is $A = 0.5\times(\text{base})\times(\text{height})$. Given base $= c - 1$, height $= 6c$ and $A=18$. Substituting these values, we get $0.5(c - 1)(6c)=18$.

Step2: Solve for $c$

First, simplify the left - hand side of the equation: $0.5\times6c(c - 1)=3c(c - 1)=3c^{2}-3c$. So the equation becomes $3c^{2}-3c = 18$, or $c^{2}-c - 6=0$. Factoring gives $(c - 3)(c + 2)=0$. So $c=3$ or $c=-2$. Since length cannot be negative, $c = 3$.

Step3: Find the height

The height is $6c$. Substitute $c = 3$ into $6c$, we get height $=6\times3=18$ meters.

Answer:

B. $0.5(c - 1)(6c)=18$; height $=18$ meters