A rectangular field is 64 m X 25 m. Shawn wants to fence a square field that has the same area as the rectangular field. How long are the sides of the square field? Please explain the thinking behind your solution strategy.
The area of the original field = 1600 m^2
so you want a square that has an area of 1600
let each side be x m
x^2 = 1600
x = 40
Area of rect.
To find the length of the sides of the square field, we need to determine the area of the rectangular field and then find the square root of that area.
Step 1: Find the area of the rectangular field.
The area of a rectangular field is calculated by multiplying its length by its width.
Area of the rectangular field = length × width
= 64 m × 25 m
= 1600 m²
Step 2: Find the square root of the area of the rectangular field.
Since the square field has the same area, we need to find the square root of the rectangular field's area.
√(1600 m²) = 40 m
Therefore, the length of each side of the square field is 40 meters.
To find the length of the sides of the square field that has the same area as the given rectangular field, we can use the concept of area.
First, let's find the area of the rectangular field:
The area of a rectangle is calculated by multiplying its length and width.
Area of the rectangular field = Length × Width
= 64 m × 25 m
= 1600 m²
Since the square field has the same area as the rectangular field, we need to find the square root of the area. The square root of the area will give us the length of each side of the square.
So, taking the square root of 1600 m²:
Side length of the square field = √(Area of the rectangular field)
= √(1600 m²)
= 40 m
Therefore, the sides of the square field would be 40 meters each.
The strategy behind this solution is to understand that two shapes have equal areas if the areas of both shapes are the same. By finding the area of the given rectangular field and taking the square root of that area, we can determine the length of the sides of the square field.