Find the area of (3×+5) and (3x+5) if its perimeter is 142cm

The perimeter of a square is $P = 4s$, where $s$ is the side length.
Given $s = (3x+5)$ and $P = 142\ \text{cm}$.

$$4(3x+5) = 142$$

$$12x + 20 = 142$$ $$12x = 142 - 20$$ $$12x = 122$$ $$x = \frac{122}{12}$$ $$x = \frac{61}{6}$$

Substitute the value of $x$ back into the side length expression $s = 3x+5$.

$$s = 3\left(\frac{61}{6}\right) + 5$$ $$s = \frac{61}{2} + 5$$ $$s = 30.5 + 5$$ $$s = 35.5\ \text{cm}$$

The area of a square is $A = s^2$.

$$A = (35.5)^2$$ $$A = 1260.25\ \text{cm}^2$$

The area of the square is $1260.25\ \text{cm}^2$.