erica painted a picture of her dog the picture has an area of 3,600 cm2 and is a square. she has placed the picture in a frame that is 5 cm wide. what is the perimeter of the picture frame?
A = lw
3600 = 5l
3600/5 = 5l/5
l = 720 cm
w = 5 cm
p = 2 l + 2w
p = 2(720) + 2(5)
p = 1450 cm
To find the perimeter of the picture frame, we need to determine the dimensions of the square picture.
Since the area of the picture is given as 3,600 cm², and the picture is a square, we can find the length of each side by taking the square root of the area.
Square root of 3,600 cm² = √3600 cm² = 60 cm
So, the length of each side of the square picture is 60 cm.
Now, the frame is 5 cm wide, which means it will add 5 cm to each side of the picture. Therefore, the dimensions of the picture frame will be:
Length = Length of the picture + 2 * width of the frame = 60 cm + 2 * 5 cm = 60 cm + 10 cm = 70 cm
Width = Width of the picture + 2 * width of the frame = 60 cm + 2 * 5 cm = 60 cm + 10 cm = 70 cm
Since the frame is square, each side of the frame will be 70 cm.
Finally, to calculate the perimeter of the picture frame, we sum up the lengths of all four sides:
Perimeter = Length + Width + Length + Width = 70 cm + 70 cm + 70 cm + 70 cm = 280 cm
Therefore, the perimeter of the picture frame is 280 cm.