I had 12 of these problems got through all but the last one.
I need to show the steps
The Parkhursts used 160 yd of fencing to enclose a rectangular corral to divide it into two paths by a fence parallel to one of the shorter sides. Find the dimensions of the corral if its area is 1000 yd ^2 ( yd has a small 2 above the d)
show each step
Do you mean two parts instead of two paths? Is the 160 yards supposed to include the outer perimeter?
If so,
3a + 2b = 160 (a is the short side)
ab = 1000
Solve the simulataneous equations.
I am having problems with the steps in this problem you are correct I made a typo it is parts - not path
thanks sam
The first equation I wrote says that the lotal length of fencing equals 160 yards. The second says the total area of the divided corral is 1000 yard^2. The rest of the problem becomes an exercise in solving simultaneous equations. Substitute 1000/a for b in the first equation and you will have an equation for a only.
3a + 2000/a = 160
Try to do the remaining steps yourself. Hint: convert to a quadratic equation). We will be glad to critique your work.
To find the dimensions of the corral, we need to set up and solve an equation based on the given information.
Let's assume that the two shorter sides of the rectangular corral are x yards each, and the longer side is y yards. We know that the area of the corral is 1000 square yards, so we have the equation:
x * y = 1000 (Equation 1)
We also know that 160 yards of fencing is used to enclose the corral, considering the two shorter sides, the longer side, and the dividing fence. Therefore, the perimeter of the corral is:
2x + y + x = 160 (Equation 2)
Now, let's solve these equations step by step:
Step 1: Solve Equation 2 for y:
2x + y + x = 160
3x + y = 160
y = 160 - 3x (Equation 3)
Step 2: Substitute Equation 3 into Equation 1:
x * (160 - 3x) = 1000
160x - 3x^2 = 1000
Rearrange the equation: 3x^2 - 160x + 1000 = 0 (Equation 4)
Step 3: Solve Equation 4 by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For Equation 4, a = 3, b = -160, and c = 1000. Plugging these values into the quadratic formula, we get:
x = (-(-160) ± √((-160)^2 - 4 * 3 * 1000)) / (2 * 3)
Simplifying further:
x = (160 ± √(25600 - 12000)) / 6
x = (160 ± √13600) / 6
x = (160 ± 116.6) / 6
This gives two possible values for x:
x1 = (160 + 116.6) / 6 = 276.6 / 6 ≈ 46.1
x2 = (160 - 116.6) / 6 = 43.4 / 6 ≈ 7.2
Step 4: Substitute each value of x back into Equation 3 to find the corresponding value of y:
For x = 46.1:
y = 160 - 3 * 46.1
y ≈ 160 - 138.3
y ≈ 21.7
For x = 7.2:
y = 160 - 3 * 7.2
y ≈ 160 - 21.6
y ≈ 138.4
So, we have two sets of dimensions for the corral:
1) x = 46.1 yards, y = 21.7 yards
2) x = 7.2 yards, y = 138.4 yards