The area of a yard is 15000 ft^2. If the ratio of the lenght to the width of the yard is 3:2, what are the dimensions of the yard?
Width = X Ft.
Length = 3X/2 Ft.
Area = (3x/2) * X = 15,000 Ft^2
Multiply both sides by 2:
3x * x = 30.000
3x^2 = 30000
x^2 = 10000
X = 100 Ft^2.
3x/2 = (3*100)/2 = 150 Ft^2
To find the dimensions of the yard, we need to use the given information and set up an equation based on the ratios.
Let's assume the length of the yard is 3x and the width is 2x. Now we can set up an equation to find the value of x.
Area of the yard = Length × Width
15000 ft^2 = (3x) × (2x)
15000 ft^2 = 6x^2
To solve for x, divide both sides of the equation by 6:
15000 ft^2 / 6 = x^2
2500 ft^2 = x^2
Taking the square root of both sides, we get:
x = √2500
x = 50
Now that we have the value of x, we can substitute it back into the expressions for length and width to get the actual dimensions of the yard:
Length = 3x = 3 × 50 = 150 ft
Width = 2x = 2 × 50 = 100 ft
Therefore, the dimensions of the yard are 150 ft by 100 ft.