An artist wants to frame a square painting with an area of 400 square inches. She wants to know the length of the wood trim that is needed to go around the painting.
a. If x is the length of one side of the painting, what equation can you set up to find the length of a side? How many solutions does the equation have?
b. Do all of the solutions that you found make sense in the context of the problem? Explain.
c. What is the length of the wood trim needed to go around the painting?
Please help me ASAP, thank you.
dumb butt
LOL I figured it out right after I sent this the answer is 20, -20, and 80.
If x is the length one side of the painting what equation can you set up to find the length of a side
a. To find the length of a side of the square painting, we can set up the equation as follows:
x * x = 400
This equation represents the area of the square painting, which is given as 400 square inches. By multiplying the length of one side (x) by itself (x * x), we get the area. This equation is a quadratic equation and can be simplified to:
x^2 = 400
To solve this equation, we can take the square root of both sides:
√(x^2) = √400
This gives us two possible solutions:
x = 20 or x = -20
However, since we are considering the length of a side of a square, we can discard the negative solution as it is not physically meaningful in this context.
Therefore, the equation x^2 = 400 has one solution, which is x = 20.
b. Yes, the solution x = 20 makes sense in the context of the problem. Since all sides of a square are equal, a side length of 20 inches satisfies the requirement of a square painting with an area of 400 square inches.
c. To find the length of the wood trim needed to go around the painting, we need to calculate the perimeter of the square painting. The perimeter of a square is given by the formula:
Perimeter = 4 * side length
In this case, the side length of the square painting is 20 inches. Therefore, we can substitute this value into the formula:
Perimeter = 4 * 20 = 80 inches
So, the length of the wood trim needed to go around the painting is 80 inches.