The dimensions are 20 ft by 50 ft the garden is to be increased by equal amounts. The new area will increase by 1800 Sq ft.
SO the new dimensions would be 40 x70 this would equal 2800 Sq ft???????
Is the initial area 1000 sq feet?
Yes, 2800 square feet.
To determine the new dimensions of the garden, we need to find the amount by which each side will be increased. Let's call this amount "x".
From the given information, the current dimensions of the garden are 20 ft by 50 ft, which means the current area is 20 ft x 50 ft = 1000 sq ft.
We know that the new area will increase by 1800 sq ft, so the new area will be 1000 sq ft + 1800 sq ft = 2800 sq ft.
To find the new dimensions, we can set up an equation using the formula for the area of a rectangle:
New length * New width = New area
Let's plug in the values we know:
(20 ft + x) * (50 ft + x) = 2800 sq ft
Expanding this equation gives us:
1000 + 70x + x^2 = 2800
Rearranging the equation to standard quadratic form, we get:
x^2 + 70x + 1000 - 2800 = 0
Simplifying further, we have:
x^2 + 70x - 1800 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. After solving, we find that x has two solutions: -90 and 20. Since the dimensions cannot be negative, we discard -90 as a solution.
Therefore, the increase in each side is 20 ft.
Using this information, we can calculate the new dimensions of the garden:
New length = 20 ft + 20 ft = 40 ft
New width = 50 ft + 20 ft = 70 ft
So the new dimensions of the garden would be 40 ft by 70 ft, which does indeed result in an area of 2800 sq ft.