If the length of each side of a square is increased by 3 cm, the perimeter of the new
square is 40 more than twice the length of each side of the original square. Find the
dimensions of the original square.
Side of original square ---- x cm
perimeter = 4x
side of new square = x+3
New perimeter = .....
translate: "the perimeter of the new
square is 40 more than twice the length of each side of the original square"
---> new perimeter you found above = 2x + 40
solve for x
so what would I set this to?
2x+40 equals what?
is the ultimate answer
side=6.5
perimeter=26?
I had assumed you found the new perimeter to be
4(x+3)
= 4x + 12
so 4x + 12 = 2x+40
I had formed that equation for you, no solve it.
Why did the square go on a diet? Because it wanted to become a smaller square! Okay, let's solve this math problem.
Let's assume the original square has a side length of "x" cm. When each side is increased by 3 cm, the new square will have a side length of "x + 3" cm.
The perimeter of the new square is equal to 4 times the side length, so it is 4(x + 3) cm.
According to the problem, this new perimeter is 40 more than twice the length of each side of the original square. So we can write the equation as:
4(x + 3) = 2x + 40
Now, let's solve this equation to find the value of "x", which will be the side length of the original square.
Let's first define the dimensions of the original square. Suppose the length of each side of the original square is "x" cm.
If the length of each side of a square is increased by 3 cm, then the length of each side of the new square becomes "x + 3" cm.
The perimeter of a square is calculated by multiplying the length of one side by 4. Therefore, the perimeter of the original square is 4x cm, and the perimeter of the new square is 4(x + 3) cm.
According to the problem, the perimeter of the new square is 40 more than twice the length of each side of the original square. Mathematically, this can be represented as:
4(x + 3) = 2x + 40
Now, let's solve this equation to find the value of "x," which is the length of each side of the original square.
Distribute 4 on the left side of the equation:
4x + 12 = 2x + 40
Move 2x to the left side and 12 to the right side:
4x - 2x = 40 - 12
2x = 28
Divide both sides of the equation by 2:
x = 28/2
x = 14
Therefore, the dimensions of the original square are 14 cm on each side.