A framer at a photo gallery wants to frame a print with a matte of uniform width all around the print. To make it pleasing to the eye, the area of the matte should equal the area of the print. If the print measures 40 cm by 60 cm, how wide should the matte be?

To find the width of the matte, we need to find the area of the print and then divide it by the perimeter of the print.

The area of the print is given by:
Area = Length x Width.
Area = 40 cm x 60 cm.
Area = 2400 cm².

The perimeter of the print is given by:
Perimeter = 2(Length + Width).
Perimeter = 2(40 cm + 60 cm).
Perimeter = 2(100 cm).
Perimeter = 200 cm.

Since the area of the matte should be equal to the area of the print, and the area should be equal to the perimeter times the width of the matte, we can set up the following equation:

2400 cm² = 200 cm x Width.

To solve for the width, divide both sides of the equation by 200 cm:

Width = 2400 cm² / 200 cm.
Width = 12 cm.

Therefore, the matte should be 12 cm wide.

To find the width of the matte, we need to first determine the dimensions of the overall frame, and then subtract the dimensions of the print from it.

Given that the print measures 40 cm by 60 cm, we can calculate the area of the print:

Area of the print = length of the print * width of the print
= 40 cm * 60 cm
= 2400 cm^2

Since the area of the matte should equal the area of the print, the area of the frame should be twice that of the print (to account for the area of the print plus the matte).

Area of the frame = 2 * Area of the print
= 2 * 2400 cm^2
= 4800 cm^2

Let's assume that the width of the matte is x cm.

Now we can calculate the dimensions of the overall frame:

Length of the frame = length of the print + 2 * width of the matte
= 40 cm + 2x cm

Width of the frame = width of the print + 2 * width of the matte
= 60 cm + 2x cm

Since the area of the frame should be 4800 cm^2, we can set up an equation:

Area of the frame = Length of the frame * Width of the frame
4800 cm^2 = (40 cm + 2x cm) * (60 cm + 2x cm)

Now we can solve this equation to find the value of x, which will give us the width of the matte.

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