Find the area of this triangle.
1 answer:
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Answer:
The area of the smallest section is
The area of the largest section is
The area of the remaining section is
Step-by-step explanation:
Please see the picture below.
1. First we are going to name the side of the larger square as x.
As the third section shares a side with the larger square and the four sides of a square are equal, we have the following:
- Area of the first section:
- Area of the second section:
(Eq.1)
- Area of the third section:
(Eq.2)
2. The problem says that the total area of the enclosed field is 975 square yards, and looking at the picture below, we have:
Replacing values:
Solving for x:
3. Replacing the value of x in Eq.1 and Eq.2:
- From Eq.1:
- From Eq.2:
The two problems are almost identical: you have to set up a system, and then solve it.
In the first case, let and
be, respectively, the number of girls and boys.
We know that (the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that
(there are 61 students in total).
So, we have the system
We can use the first equation to substitute in the second
And then solve for :
For the second problem, let and
be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system
And you can solve it in the very same way we solved the previous one.