the ratio of the lengths of the corresponding sides of two rectangles is 8:3. The area of the larger rectangle is 320 ft^2. What is the area of the smaller rectangle?
8/3 = sqrt(320)/sqrt(A2)
Cross multiply:
8*sqrt(A2) = 3*sqrt(320)
Divide both sides by 8:
sqrt(A2) = 3*sqrt(320) / 8
Square both sides:
A2 = 45 Ft.^2.
two number are in the ratio 9:2 .if the smaller number is 320 .find the larger number
To find the area of the smaller rectangle, we need to use the given ratio of the lengths of the corresponding sides.
Let's assume the length of the larger rectangle is 8x and the length of the smaller rectangle is 3x.
Since the ratio of their lengths is given as 8:3, we can conclude that the width of the larger rectangle would be 8x * (3/8) = 3x.
Now that we have the length and width of the smaller rectangle, we can find its area. The area of a rectangle is determined by multiplying its length and width.
Area of smaller rectangle = Length * Width = 3x * 3x = 9x^2.
Next, we are given that the area of the larger rectangle is 320 ft^2. We can use this information to solve for x.
Area of larger rectangle = Length * Width = 8x * 3x = 320 ft^2.
Now, we can solve for x:
24x^2 = 320
Divide both sides by 24:
x^2 = 320/24
x^2 = 13.3333...
To find x, we can take the square root of both sides:
x = √(13.3333...) ≈ 3.6514
Now, we can substitute the value of x back into the equation to find the area of the smaller rectangle:
Area of smaller rectangle = 9x^2 = 9 * (3.6514)^2 ≈ 121.6704 ft^2.
Therefore, the area of the smaller rectangle is approximately 121.6704 square feet.