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? divide the area by 2, and then multiply the quotient by 4. set the area equal to x², solve for x, and then multiply the value of x by 4. set the area equal to x³, and then solve for x. set the area equal to x², solve for x, and then divide the value of x by 4

Explanation:

Step1: Recall square - area and perimeter formulas

The area formula for a square is $A = s^{2}$, where $s$ is the side - length of the square, and the perimeter formula is $P=4s$.

Step2: Solve for side - length from area

If the area of the square picture is $A$, and $A = s^{2}$, then $s=\sqrt{A}$.

Step3: Calculate the perimeter

The amount of framing material needed is equal to the perimeter of the square picture. Since $P = 4s$, substituting $s=\sqrt{A}$ into the perimeter formula, we get $P = 4\sqrt{A}$. In the given steps, if we set the area equal to $x^{2}$ (i.e., $A=x^{2}$), then $x = s$ (the side - length of the square), and multiplying $x$ by 4 gives the perimeter.

Answer:

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