Hi!
Your answer is the first option, 0.17.
To solve this, we will have to do a few things.
- Solve for the area of the triangle
- Solve for the area of the rectangle
- Find what percent the area of the triangle is of the area of the rectangle
STEP ONE
Area of a triangle: [tex]area=\cfrac{base*height}{2}[/tex]
Use the given values to plug it into the formula:
[tex]area=\cfrac{4*6}{2}[/tex]
[tex]area=\frac{24}{2}[/tex]
[tex]area=12[/tex]
The area of the triangle is 12 centimeters squared.
STEP TWO
Area of a rectangle: [tex]area=length*width[/tex]
Use the given values to plug it into the formula:
[tex]area=10*7[/tex]
[tex]area=70[/tex]
The area of the rectangle is 70 centimeters squared.
STEP THREE
To do this step, we must divide the area of the triangle by the area of the rectangle.
This will give us the percent that the triangle is of the rectangle, and hence will give us the probability of it landing inside of the rectangle.
So:
[tex]12/70=0.17[/tex]
Therefore, the probability that a point chosen randomly inside the rectangle is in the triangle is 0.17.
