The side of 2 square fields are in the ratio of 3:5.the area of the larger field is 576m^2 greater than the area of the smaller field .Find the area of this smaller field?
Ddgg
To solve this problem, let's assume the smaller square field has a side length of 3x, and the larger square field has a side length of 5x (since their sides are in the ratio of 3:5).
The area of a square is equal to the square of its side length. Therefore, the area of the smaller field is (3x)^2 = 9x^2.
According to the problem, the area of the larger field is 576m^2 greater than the area of the smaller field. So we can set up the equation:
Area of larger field - Area of smaller field = 576m^2
(5x)^2 - (3x)^2 = 576m^2
25x^2 - 9x^2 = 576m^2
16x^2 = 576m^2
Divide both sides of the equation by 16:
x^2 = 36m^2
Now, take the square root of both sides to find the value of x:
x = √(36m^2)
x = 6m
Since x represents the side length of the smaller square field, the area of the smaller field is:
Area = (3x)^2 = (3 * 6m)^2 = 54m^2
Therefore, the area of the smaller field is 54m^2.
To find the area of the smaller field, we'll need to set up and solve an equation based on the given information.
Let's assume that the side lengths of the smaller and larger fields are 3x and 5x, respectively. The ratio of their side lengths is 3:5.
Therefore, the area of the smaller field can be represented as (3x)^2 = 9x^2.
Given that the larger field's area is 576m^2 greater than the smaller field's area, we can express the area of the larger field as 9x^2 + 576.
Now, we can set up an equation: 9x^2 + 576 = 5x^2.
Rearranging this equation, we get 9x^2 - 5x^2 + 576 = 0.
Simplifying, we have 4x^2 = 576.
Dividing both sides by 4, we get x^2 = 144.
Taking the square root of both sides, we find x = 12.
Since we assumed that the side length of the smaller field is 3x, the side length of the smaller field is 3 * 12 = 36 meters.
Finally, to find the area of the smaller field, we square the side length: 36^2 = 1296 m^2.
Therefore, the area of the smaller field is 1296 square meters.
the ratio of the areas is the square of the ratio of the sides ... 3^2 : 5^2 ... 9 : 25
25 a / 9 = a + 576