Question

9 multiple choice 1 point which of the following represents the height of a triangle, in meters, that has a base length of 36 meters and the same area as a square that has a side length of 12 meters? reference sheet a = πr² c = 2πr a = lw a = 1/2bh c²=a² + b² special right triangles v = lwh v = πr²h v = 4/3πr³ v = 1/3πr²h v = 1/3lwh the number of degrees of arc in a circle is 360. the number of radians of arc in a circle is 2π. the sum of the measures in degrees of the angles of a triangle is 180. 8 432 4 12

Explanation:

Step1: Calculate square area

The area formula for a square is $A = s^2$, where $s$ is the side - length. Given $s = 12$ meters, so $A_{square}=12^2=144$ square meters.

Step2: Set up triangle area equation

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. We know $A_{triangle}=A_{square}=144$ square meters and $b = 36$ meters. Substitute into the formula: $144=\frac{1}{2}\times36\times h$.

Step3: Solve for height $h$

First, simplify the right - hand side of the equation: $\frac{1}{2}\times36\times h = 18h$. Then, solve the equation $144 = 18h$ for $h$. Divide both sides by 18: $h=\frac{144}{18}=8$ meters.

Answer:

8