I am so tired and I need help as soon as possible please with my Algebra homework

Question

Question 1: What is the probability that a point chosen randomly inside the rectangle is in the square?

A.) 1/6

B.) 3/77

C.) 3/154

D.) 9/308

help me

Answer 1

Hi, Jake!

So, for this particular type of question, what you need to do is start by finding the area of the larger space. The area of the rectangle is the larger space and contains the other 3 shape. Also, know that because we are trying to find the probability of something that we will be dealing with fractions/proportions/ratios here. What is the whole? What are the parts?

The whole is like I said - the large rectangle

The parts are: the triangle, the square, the circle and all of the additional unused space inside the rectangle.

So, what is the area of the rectangle? It is 22 inches x 14 inches

22 x 14 = (22 x 10) + (22 x 4) = 220 + 88 = 308 inches²

Now, we would normally find the areas of all of the other 3 shapes for a question like this, but since they have specified the square, that is all we need to be concerned with. What is the area of the square?

3 inches x 3 inches = 3 x 3 = 9 inches²

So the probability that if you closed your eyes and picked any random point inside the rectangle, that the point would be inside or on the square is

the area of the square ÷ the area of the rectangle = 9 ÷ 308 = about 3% probability. The answer should be D.

Does this make sense?

Answer 2

First find the area of the the whole shape, that would be 22x14=308. Now we just need to find the are of the square, which is A=side x side= 3x3= 9.

So the probability would be "9/308"