A rock climber averages 12 3/5 feet per minute. Write and solve an equation to find how many feet x the rock climber climbs in 3
1 answer:
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First, we need to find the length of the side of the square.
Use phytagorean theorem to find the length of the side. The side acts as hypotenuse, the distance of x and the distance of y acts as the perpendicular side of a right triangle. For clear understanding, see image attached.
General phytagorean theorem
c² = a² + b²
c represents hypotenuse, a and b are the side perpendicular to each other.
In this case, we could write it as
s² = Δx² + Δy²
s represents the length of the side, Δx represents distance of x, Δy represents distance of y
Plug in the numbers, use two of the vertices
I use (4,-1) and (7,3)
s² = Δx² + Δy²
s² = (7-4)² + (3 - (-1))²
s² = 3² + (3 + 1)²
s² = 3² + 4²
s² = 9 + 16
s² = 25
s = √25
s = 5
The length of the side is equal to 5 units length.
Second, find the area of the square
General area to find the area of a square
a = s²
Plug in the numbers
a = s²
a = 5²
a = 25
The area of the square is equal to 25 units area.
Use phytagorean theorem to find the length of the side. The side acts as hypotenuse, the distance of x and the distance of y acts as the perpendicular side of a right triangle. For clear understanding, see image attached.
General phytagorean theorem
c² = a² + b²
c represents hypotenuse, a and b are the side perpendicular to each other.
In this case, we could write it as
s² = Δx² + Δy²
s represents the length of the side, Δx represents distance of x, Δy represents distance of y
Plug in the numbers, use two of the vertices
I use (4,-1) and (7,3)
s² = Δx² + Δy²
s² = (7-4)² + (3 - (-1))²
s² = 3² + (3 + 1)²
s² = 3² + 4²
s² = 9 + 16
s² = 25
s = √25
s = 5
The length of the side is equal to 5 units length.
Second, find the area of the square
General area to find the area of a square
a = s²
Plug in the numbers
a = s²
a = 5²
a = 25
The area of the square is equal to 25 units area.
To answer this question, we need to recall that: "the diagonals of a rectangle bisect each other"
Thus, if we assign the point of intersection of the two diagonals in the rectangle as point O, we can say that the triangle OQR is an "isosceles triangle". Note that this is because the lengths OR and OQ are equal since we know that: "the diagonals of a rectangle bisect each other". See the below diagram for clarity.
Now, we have to recall that:
- the base angles of any isosceles triangle are equal. This is a fact, and this means that the angles
- also the sum of all the angles in any triangle is 180 degrees
Now, considering the isosceles triangle OQR, we have that:
Now, since the figure already shows that angle Now, since we have established that the base angles
we can now solve the above equation for m<2 as follows:
Therefore, the correct answer is: option D
