Judy made a rectangular shaped figure of dimensions 20cm by 5cm with a piece of clay . She then took the same amount of clay and made a square figure. If the thickness of the square is the same as that of the rectangle, calculate the length of one side of the square figure ?
Plz help me understand this
Area of rectangle =
A = LW
A - 20 * 5
A = 100 square cm.
√100 = 10 = each side of square
Area of Rectangle:
A = LW
A = (20cm)(5cm)
A = 100 cm^2
Area of Square:
A = s^2, where s = side of square
100 = s^2
sqrt{100} = {s^2}
10 cm = s
To solve this problem, we need to understand that the volume of the clay used to make the rectangular shape is equal to the volume of the clay used to make the square shape.
The volume of the rectangular shape can be calculated by multiplying the length, width, and height (thickness) together. In this case, the length is 20cm, the width is 5cm, and the height (thickness) is given as the same for both shapes.
So, the volume of the rectangular shape is 20cm x 5cm x h, where 'h' is the height (thickness) of the shape.
Now, if the same amount of clay is used to make the square shape, the volume will be h x s x s, where 's' is the length of one side of the square shape.
Since the volumes are equal, we can set up the equation:
20cm x 5cm x h = h x s x s
We can now simplify the equation:
100cm^2h = h x s^2
By canceling out 'h', we get:
100cm^2 = s^2
To find the length of one side of the square figure, we take the square root of both sides:
sqrt(100cm^2) = sqrt(s^2)
s = sqrt(100cm^2)
s = 10cm
Therefore, the length of one side of the square figure is 10cm.