The area of square is 144cm^ and one of its sides (x+2)cm.find x and then the side of the square
Let's solve this step by step.
Since we know that the area of the square is 144 cm^2, we can use the formula for the area of a square, which is side^2. So, we have:
(side)^2 = 144
We also know that one of the sides is (x+2) cm. Substituting this into the equation, we have:
(x+2)^2 = 144
Expanding the equation, we get:
x^2 + 4x + 4 = 144
Rearranging the equation, we get:
x^2 + 4x - 140 = 0
Factoring the equation, we get:
(x + 14)(x - 10) = 0
Setting each factor to zero and solving for x, we have:
x + 14 = 0 or x - 10 = 0
x = -14 or x = 10
Since the length of a side cannot be negative, we disregard the solution x = -14.
Therefore, x = 10.
To find the side of the square, we substitute x = 10 into the side length equation: side = x + 2.
side = 10 + 2 = 12 cm
So, the side of the square is 12 cm.