A rectangle is ( x+2)cm long and 5cm wide if a square of side x cm has the same perimeter as thet of the rectangle what is the length of the side of the square?
Yes
2 (x + 2) + 2 (5) = 4 (x) ... 2 x + 4 + 10 = 4 x
solve for x
To find the length of the side of the square, we first need to calculate the perimeter of both the rectangle and the square.
Perimeter of Rectangle:
The formula to calculate the perimeter of a rectangle is given by P = 2(l + w), where P is the perimeter, l is the length, and w is the width of the rectangle.
Given that the length of the rectangle is (x+2) cm and the width is 5 cm, we can substitute these values into the formula:
P_rectangle = 2((x+2) + 5) = 2(x+7) cm
Perimeter of Square:
For a square, all four sides are of equal length. Let's assume the length of one side of the square is s cm.
The formula to calculate the perimeter of a square is given by P = 4s, where P is the perimeter and s is the length of one side of the square.
Since the perimeter of the square is equal to the perimeter of the rectangle, we can equate the two formulas:
2(x+7) = 4s
Now we can solve for s, which is the length of one side of the square.
2(x+7) = 4s
Divide both sides of the equation by 2:
(x+7) = 2s
Subtract 7 from both sides of the equation:
x = 2s - 7
Therefore, the length of the side of the square is 2s - 7 cm.