using L as the length and W is wide asume L is great then W . If a architect is makiing a swimming pool to go into a rectangular area of fencing and she uses 6 yards of fencing to enclose a rectangular area of 352 square yards what would the dinension be for L and W?
Is your 6 yards of fencing a misprint? That is not enough to enclose the required area.
yes it iws suppose to be 60 sorry
Then L*W = 352 and
2(L + W) = 60
Solve the two simultaneous equations. Let L = 352/W
2(352/W +W) = 60
(352/W) + W = 30
W^2 - 30W + 352 = 0
There is no real solution. 60 yards of fencing is not enough to enclose 352 sq. yards. You need at least 75 yards
To find the dimensions of the rectangular area (L and W) given the perimeter and area, follow these steps:
Step 1: Understand the problem and gather the given information.
- The perimeter (the amount of fencing used) is 6 yards.
- The area of the rectangular area to be enclosed is 352 square yards.
- L (length) is greater than W (width).
Step 2: Set up an equation using the given information.
- The perimeter of a rectangle is calculated by adding all four sides: P = 2L + 2W.
- Since L is greater than W, we can write L = W + x, where x is the additional length.
Step 3: Solve for L and W using the equation.
- Substitute L = W + x into the perimeter equation: 2(W + x) + 2W = 6.
- Simplify the equation: 2W + 2x + 2W = 6.
- Combine like terms: 4W + 2x = 6.
- Divide both sides by 2 to isolate W: 2W + x = 3.
- Rearrange the equation: x = 3 - 2W.
Step 4: Find the additional length (x).
- Since L is greater than W, L = W + x. Substitute the value of x obtained in the previous step: L = W + (3 - 2W).
- Simplify the equation: L = 3 - W.
Step 5: Calculate the area using the obtained dimensions.
- The area of a rectangle is calculated by multiplying length and width: A = L * W.
- Substitute the values of L and W: 352 = (3 - W) * W.
Step 6: Solve the quadratic equation to find the values of W.
- Multiply out the equation: 352 = 3W - W^2.
- Rearrange the equation: W^2 - 3W + 352 = 0.
- Solve the quadratic equation using factoring, completing the square, or using the quadratic formula.
Once you find the possible values of W, plug them back into the equation L = 3 - W to obtain the corresponding lengths (L) for each width (W).