Find the area of a square that has the same perimeter as a rectangle whose length is 48m and the ratio of length to the breadth is 3:1.
3/1 = 48/x
48/3 = 16
P = 2(48) + 2(16)
P = 128
128/4 = 32
A = 32^2
A = 1,024 sq. m
Thanks for answer
To find the area of the square, we need to determine the length of its sides.
Given that the length of the rectangle is 48m and the ratio of length to breadth is 3:1, we can find the breadth of the rectangle by dividing the length by the sum of the ratio's parts:
Breadth = (1 / (3 + 1)) * 48m = (1 / 4) * 48m = 12m.
Since the perimeter of the square is equal to the perimeter of the rectangle, we can calculate the perimeter of the rectangle using its length and breadth:
Perimeter of the rectangle = 2 * (length + breadth) = 2 * (48m + 12m) = 2 * 60m = 120m.
Since the square has the same perimeter as the rectangle, its perimeter is also 120m.
The perimeter of a square is given by P = 4s, where s is the length of each side.
Therefore, 4s = 120m.
Dividing both sides of the equation by 4, we get:
s = 120m / 4 = 30m.
Now that we know the length of each side of the square is 30m, we can find its area by squaring the length of one side:
Area of the square = side * side = 30m * 30m = 900 square meters.
Therefore, the area of the square with the same perimeter as the given rectangle is 900 square meters.