If two sides of a square field were incresed by three feet the area of the field would increase by 129 square feet. find the area of the original field.
If two sides of a square field were incresed by three feet the area of the field would increase by 129 square feet. find the area of the original field.
Let x be the side of the original square field.
Then, (x + 3)^2 - x^2 = 129
x^2 + 6x + 9 - x^2 = 129
6x = 120 making x = 20.
Therefore, the area of the original square is 20^2 == 400 sq. ft.
Why did the square field go on a diet? Because it wanted to increase its area by 129 square feet! The original area of the field is 400 square feet.
To find the area of the original field, we can use the formula for the area of a square, which is side length squared. Let's let x be the side length of the original square field.
According to the given information, if two sides of the square field are increased by three feet, the area of the field increases by 129 square feet.
We can set up the equation: (x + 3)^2 - x^2 = 129.
Expanding the equation, we get: x^2 + 6x + 9 - x^2 = 129.
Simplifying the equation, we get: 6x + 9 = 129.
To isolate x, we can subtract 9 from both sides of the equation: 6x = 120.
Dividing both sides of the equation by 6, we get: x = 20.
Therefore, the side length of the original square field is 20 feet.
To find the area of the original field, we square the side length: 20^2 = 400 square feet.
Therefore, the area of the original field is 400 square feet.
To find the area of the original field, we can set up an equation using the given information.
Let x be the side length of the original field.
According to the problem, if two sides of the square field were increased by three feet, the area would increase by 129 square feet.
The new side length of the field would be (x + 3) and the new area would be (x + 3)^2.
We can set up the equation:
(x + 3)^2 - x^2 = 129
Expanding the equation, we get:
x^2 + 6x + 9 - x^2 = 129
The x^2 terms cancel out, leaving us with:
6x + 9 = 129
Subtracting 9 from both sides, we get:
6x = 120
Dividing both sides by 6, we find:
x = 20
Therefore, the side length of the original field is 20 feet.
To find the area of the original square, we square the side length:
Area = x^2 = 20^2 = 400 square feet.
So, the area of the original field is 400 square feet.