Gery wants to fence a rectangular field whose area is 1200 sq.m. He has only 100 meters of fencing so he decided to fence only the three side of the rectangle letting the wall be the fourth side. How wide the rectangle should be?
let the length of the single side by y
let each of the other two sides be x
so you have y + 2x = 100 , ----> y = 100-2x
area = xy = x(100-2x)
= -2x^2 + 100x
this is a downwards opening parabola.
Find the vertex, the x of the vertex is the length of one of the two equal sides.
Let me know what you got
I don't even know sir
To be able to do this question, you MUST be studying parabolas.
Have you learned about "completing the square" ?
Do you know that for y = ax^2 + bx + c, the x of the vertex is -b/(2a) ?
Trying to find out where your difficulties lie.
I can't understand that kind of solution sir, please help me to solve this so that I can study this problem. Please sir?
sir?
I have to know what topic you are studying now in math, and at what level or grade . Please answer my two previous questions so I can even begin to help you.
To find the width of the rectangle, we need to start by defining the variables in the problem.
Let's say:
- Length of the rectangle = L (in meters)
- Width of the rectangle = W (in meters)
We know that Gery has 100 meters of fencing available, and he wants to fence three sides of the rectangle (the two lengths and one width), while the fourth side is already a wall.
So, the total length of fencing needed will be:
2L (for the lengths) + W (for the width)
According to the problem, Gery wants to fence an area of 1200 sq.m. The area of a rectangle is calculated by multiplying its length by its width, so we have:
L * W = 1200
Now we need to solve the system of equations formed by the constraints of the problem:
2L + W = 100 (equation formed by the length of the fencing)
L * W = 1200 (equation formed by the area of the rectangle)
There are a few methods to solve this system of equations, and one of the most common approaches is substitution:
From the first equation, we can express W in terms of L:
W = 100 - 2L
By substituting this value of W into the second equation, we get:
L * (100 - 2L) = 1200
Simplifying, we have:
100L - 2L^2 = 1200
Rearranging the equation, we have:
2L^2 - 100L + 1200 = 0
Now we can solve this quadratic equation for L. We can either factorize it, complete the square, or use the quadratic formula. In this case, let's use the quadratic formula:
L = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 2, b = -100, and c = 1200. Substituting these values, we have:
L = (-(-100) ± √((-100)^2 - 4 * 2 * 1200)) / (2 * 2)
L = (100 ± √(10000 - 9600)) / 4
L = (100 ± √400) / 4
L = (100 ± 20) / 4
Considering the positive root (as L cannot be negative in this context), we have:
L = (100 + 20) / 4
L = 120 / 4
L = 30 meters
Therefore, the width of the rectangle should be:
W = 100 - 2L
W = 100 - 2 * 30
W = 100 - 60
W = 40 meters
So, the rectangle should be 30 meters in length and 40 meters in width.