A rectangle and a square each have the same area. If one side of the rectangle is 9 units and one
side of the square is 6 units, how many units are in the perimeter of the rectangle?
area of both = 6*6 = 36
area of rectangle also = 36 = 9 *w
so
w = 4 and rectangle has perimeter = 9+9 + 4+4 = 18 + 8 = 26
To find the perimeter of a rectangle, we need to add the lengths of all four sides. We know that one side of the rectangle is 9 units.
Since the area of the rectangle and the square are equal, we can find the area of the square by squaring the length of one side. In this case, the side of the square is 6 units, so the area of the square is 6^2 = 36 square units.
Since the area of the rectangle is also 36 square units, we can use the formula for the area of a rectangle, which is length multiplied by width. Let's represent the width of the rectangle as W.
So, 9W = 36.
Dividing both sides of the equation by 9 to solve for W, we get:
W = 4.
Therefore, the width of the rectangle is 4 units.
Now that we know both the length and width of the rectangle, we can calculate the perimeter by adding all four sides:
Perimeter = 2(length + width)
= 2(9 + 4)
= 2(13)
= 26 units.
Therefore, the perimeter of the rectangle is 26 units.
To find the perimeter of the rectangle, we need to calculate the sum of all its sides.
We know that one side of the rectangle is 9 units, but we don't know the length of the other side. However, we are given that the rectangle and the square have the same area.
The area of a rectangle is calculated as length × width, and the area of a square is calculated as side × side. Since the area of both the rectangle and the square is the same, we can set up the following equation:
9 × width of the rectangle = 6 × 6
Simplifying this equation, we have:
9 × width of the rectangle = 36
Dividing both sides of the equation by 9, we find:
width of the rectangle = 4
Now that we know the width of the rectangle is 4 units, we can calculate its perimeter by adding up all its sides:
Perimeter of the rectangle = 9 + 4 + 9 + 4 = 26 units
Therefore, the perimeter of the rectangle is 26 units.