Question

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.
4
8
12
432

Explanation:

Step1: Calculate square's area

$A_{square}=s^2$, where $s = 12$ meters. So $A_{square}=12^2=144$ square - meters.

Step2: Set up triangle - area equation

The area of a triangle is $A_{triangle}=\frac{1}{2}bh$, where $b = 36$ meters and $A_{triangle}=A_{square}=144$ square - meters. Substitute the values into the formula: $144=\frac{1}{2}\times36\times h$.

Step3: Solve for $h$

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

Answer:

8