Question

sachiko is framing the border of a square picture. if she knows the area of the picture, how could sachiko determine the amount of framing material she needs to buy? set the area equal to x, and then solve for x. set the area equal to x², solve for x, and then multiply the value of x by 4. divide the area by 2, and then multiply the quotient by 4.

Explanation:

Step1: Recall the formula for the perimeter of a square

For a square, if the side - length is $s$, the area $A = s^{2}$ and the perimeter $P=4s$. Given $A = x$, we first find the side - length.

Step2: Solve for the side - length

If $A = s^{2}=x$, then $s=\sqrt{x}$.

Step3: Calculate the perimeter

The perimeter $P = 4s$. Substituting $s=\sqrt{x}$ into the perimeter formula, we get $P = 4\sqrt{x}$. To find the amount of framing material (which is equal to the perimeter of the square picture), we first set the area equal to $x$, solve for $x$ (in terms of the side - length), and then multiply the side - length by 4.

Answer:

Set the area equal to $x^{2}$, solve for $x$, and then multiply the value of $x$ by 4.