Solve the problem. Round the answer to the nearest hundredth. Please Show All Work!
A garden is currently 4 meters wide and 7 meters long. If the area of the garden is to be doubled by increasing the width and length by the same number of meters, find the new dimension of the garden.
Please show your work and someone will be glad to critique it. You are just dumping your problems here.
I am sorry but i do not even know how to start the problem that is why i asked for someone to answer it and show work so that i maybe able to better understand it
Let x be the amount by which both length and width are increased.
The new area is (4+x)(7+x)
Set that equal to twice the former area (2*4*7 = 56)and solve for x
6.1 and 9.1
To solve this problem, we first need to find the current area of the garden.
The area of a rectangle is calculated by multiplying its length by its width. In this case, the current width is 4 meters and the current length is 7 meters.
Area = 4 meters * 7 meters = 28 square meters
Next, we need to find the number of meters by which both the width and length will be increased to double the area of the garden. Let's call this number "x".
To double the area, we need to multiply the width and length by the same number, which is x.
Therefore, the new width will be 4 + x meters, and the new length will be 7 + x meters.
The new area will be the double of the current area, which is 28 square meters * 2 = 56 square meters.
Now we can set up an equation to find the value of x.
(4 + x) meters * (7 + x) meters = 56 square meters
Expanding the equation:
28 + 4x + 7x + x^2 = 56
Combining like terms:
x^2 + 11x + 28 - 56 = 0
x^2 + 11x - 28 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring is not easily applicable, so we'll use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 11, and c = -28.
x = (-11 ± √(11^2 - 4*1*(-28))) / (2*1)
x = (-11 ± √(121 + 112)) / 2
x = (-11 ± √(233)) / 2
Using a calculator, we can find the approximate values of x.
x ≈ (-11 + √(233)) / 2 ≈ 2.05
x ≈ (-11 - √(233)) / 2 ≈ -13.05
Since the width and length cannot be negative, we discard the negative value of x.
Therefore, the new width will be 4 + 2.05 meters ≈ 6.05 meters, and the new length will be 7 + 2.05 meters ≈ 9.05 meters.
So, the new dimensions of the garden, rounded to the nearest hundredth, are approximately 6.05 meters by 9.05 meters.