A rectangular garden measure 15m by 10m. When each side is increased by the same amount, the area of the garden is doubled. Find the dimensions of the new garden.
2(15 * 10) = 300
Can you take it from there?
Can you explain more
The original garden has 150 square meters. The new garden has 300 square meters.
Add the same number to the original dimensions so that their product is 300.
A = LW
Ok let me try that
I got
L=17.4
W= 12.4
But it's not right because when I multiply them I don't get 300
Hint: The dimensions must be multiples of 5.
I got it thank u so much
You're very welcome.
To solve this problem, we need to calculate the new dimensions of the garden after both sides are increased by the same amount.
Let's assume that the increase in length on each side is "x" meters.
The original garden has dimensions 15m by 10m, so its area is given by:
Area = length * width = 15m * 10m = 150 square meters
When each side is increased by "x" meters, the new length will be (15 + x) meters and the new width will be (10 + x) meters.
The area of the new garden should be double the area of the original garden, so we set up the equation:
2 * 150 square meters = (15 + x) meters * (10 + x) meters
Now we can solve this equation for "x":
2 * 150 = (15 + x) * (10 + x)
300 = 150 + 25x + 15x + x^2
Rearranging and simplifying:
x^2 + 40x + 150 = 0
To solve this quadratic equation, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 40, and c = 150:
x = (-40 ± √(40^2 - 4*1*150)) / 2*1
x = (-40 ± √(1600 - 600)) / 2
x = (-40 ± √1000) / 2
Now, calculating the two possible values of x:
x = (-40 + √1000) / 2 ≈ 6.47 meters
x = (-40 - √1000) / 2 ≈ -46.47 meters
Since length and width cannot be negative, we discard the negative solution.
Therefore, the increase in length and width is approximately 6.47 meters.
To find the new dimensions of the garden, we add the increase to each side of the original garden:
New length = 15m + 6.47m ≈ 21.47 meters
New width = 10m + 6.47m ≈ 16.47 meters
So the new dimensions of the garden are approximately 21.47 meters by 16.47 meters.