Question 109974
Mike drew a painting on a rectangular paper size 59 by 43 centimeter. Later he places the painting in a rectangular frame of which a uniform space is left around the painting. If the perimeter of the base of the frame is 256 centimeters. what is the width of the space that surrounds the painting?
:
Let x = the width of the space around the 59 by 43 cm painting
:
The dimensions of the frame will be:
(59+2x) by (43+2x)
:
The perimeter of the frame will be:
2(59+2x) + 2(43+2x) = 256
:
Simplify equation divide by 2:
59 + 2x + 43 + 2x = 128
:
4x + 102 = 128
:
4x = 128 - 102
:
x = 26/4
:
x = 6.5" is the width of the area around the painting
:
:
Check solution using the perimeter:
Frame: (59+13) by (43+13)
2(72) + 2(56) = 
144 + 112 = 256