Question

To put a narrow border around a square photo, Alicia has 32 inches of trim. The area of the photo is 60 square inches. Will she have enough trim for all four sides of the square? Explain how you decided.

Answer 1

Answer: Yes, she will have enough trim for all four sides of the square, because the perimeter of the square photo (30.98 inches) is less than  32 inches of trim she has.

Step-by-step explanation:

The formula for calculate the area of a square is:

$A=s^2$

Where "s" is the lenght of any side of the square.

The formula for calculate the perimeter of a square is:

$P=4s$

Where "s" is the lenght of any side of the square.

We know that that the area of the photo is 60 square inches, therefore, we can solve for "s" from the formula  $A=s^2$ and find its value:

$A=s^2\\\\s=\sqrt{A}[\\\\s=\sqrt{60in^2}\\\\s=2\sqrt{15}in$

Substituting the value of "s" into the formula $P=4s$, we get that the perimeter of the photo is:

$P=4(2\sqrt{15}in)=30.98in$

Therefore, since Alicia has 32 inches of trim and $30.98in$, we can conclude that she will have enough trim for all four sides of the square.