Find the length of each side when the perimeter of the rectangle is 72 cm. one side is X and the other side is 2x+3
P = 2 a + 2 b
In your case : a = x , b = 2 x + 3
P = 2 a + 2 b = 72
P = 2 x + 2 * ( 2 x + 3 ) = 72
2 x + 4 x + 6 = 72
6x + 6 = 72 Subtract 6 to both sides
6 x + 6 - 6 = 72 - 6
6 x = 66 Divide both sides by 6
x =11
x = a = 11 cm
b = 2 x + 3
b = 2 * 11 + 3 = 22 + 3 = 25 cm
P = 2 a + 2 b
P = 2 * 11 + 2 * 25
P = 22 + 50 = 72 cm
To find the length of each side, we can set up an equation using the given information.
Let's assume one side of the rectangle is X cm, and the other side is 2X + 3 cm.
The perimeter of a rectangle is calculated by adding all four sides together. In this case, we have:
Perimeter = X + 2X + 3 + X + 2X + 3
Now, we are given that the perimeter of the rectangle is 72 cm. So, we can write the equation as:
72 = X + 2X + 3 + X + 2X + 3
Simplifying the equation, we combine like terms:
72 = 6X + 6
Next, let's isolate X by subtracting 6 from both sides:
72 - 6 = 6X + 6 - 6
66 = 6X
Finally, divide both sides by 6 to solve for X:
66/6 = 6X/6
11 = X
So, one side of the rectangle is 11 cm.
To find the other side, we substitute the value of X back into the expression 2X + 3:
2(11) + 3 = 22 + 3 = 25
Hence, the other side of the rectangle is 25 cm.