The ratio of the perimeters of two squares is 1:5. If the area of the bigger square is 250m^2, find the perimeter of the two squares
let the side of the smaller square be x
let the side of the larger square be y
4x/4y = 1/5
x/y = 1/5
y = 5x
area of larger = 250
y^2 = 250
y = √250 = 5√10
then 5x = 5√10
x = √10
perimeter = 4x + 4y
= 4√10 + 20√10 = 24√10 or appr 75.9 m
To find the perimeter of the two squares, we first need to determine the length of the sides of each square.
Let's assume that the length of the side of the smaller square is "x" meters.
Since the ratio of the perimeters of the two squares is 1:5, we can set up the following equation:
Perimeter of smaller square / Perimeter of bigger square = 1 / 5
Since the perimeter of a square is 4 times the length of its side:
4x / (4y) = 1 / 5
Where "y" represents the length of the side of the larger square.
Simplifying the equation, we get:
x / y = 1 / 5
Since the area of the bigger square is given as 250 square meters, we can determine the length of the side of the bigger square:
Area of bigger square = (side length)^2
250 = y^2
Taking the square root of both sides, we find:
y = √250
y = 15.81 meters (rounded to two decimal places)
Now, we can substitute the value of "y" into the ratio equation and solve for "x":
x / 15.81 = 1 / 5
Multiplying both sides by 15.81, we get:
x = 15.81 / 5
x = 3.16 meters (rounded to two decimal places)
Therefore, the length of the sides of the smaller square is approximately 3.16 meters, and the length of the sides of the larger square is approximately 15.81 meters.
Finally, we can calculate the perimeter of each square:
Perimeter of smaller square = 4 * x = 4 * 3.16 = 12.64 meters
Perimeter of bigger square = 4 * y = 4 * 15.81 = 63.24 meters
Hence, the perimeter of the smaller square is approximately 12.64 meters, and the perimeter of the larger square is approximately 63.24 meters.