In the square, x represents a positive whole number. find the value of x much that the area is equal to half the perimeter of the square.
Your question did not make sense the first time you posted it, that is why nobody has answered it.
Are we supposed to see some kind of square?
Does the x "in the square" represent the area or the length of the side?
Awaiting your clarification so I can answer your question.
The square simply shows an unknown number, x covering one side. Meaning x represents the length of the side.
so the area is x^2
and the perimeter is 4x
area = (1/2)perimeter
x^2 = 2x
x^2 - 2x = 0
x(x-2) = 0
x = 2 or x = 0 , the latter makes no sense
To find the value of x that satisfies the given condition, let's break down the problem step by step.
First, let's determine the expressions for the area and perimeter of the square.
The area of a square is given by the formula: A = side^2, where "side" represents the length of one side of the square.
The perimeter of a square is given by the formula: P = 4 * side.
Now, we are given that the area of the square is equal to half the perimeter. Mathematically, this can be represented as: A = (1/2) * P.
Let's substitute the formulas for A and P into the equation:
side^2 = (1/2) * 4 * side
Simplifying the equation further:
side^2 = 2 * side
Now, we can solve this quadratic equation to find the value of side (x):
x^2 = 2x
Rearranging the terms:
x^2 - 2x = 0
Factoring out x:
x(x - 2) = 0
From this equation, we can see that either x = 0 or (x - 2) = 0. Since x represents a positive whole number, x cannot be zero.
Therefore, we solve for x - 2 = 0:
x - 2 = 0
x = 2
Thus, the value of x that satisfies the given condition is 2.