Final answer:
To find the width of the uniform border around a picture, the perimeter formula is adjusted to include the border's width. Through a series of algebraic steps, it is determined that the border's width is 2 inches.
Step-by-step explanation:
The student is asking how to find the width of the uniform border surrounding an 8 x 10 picture given that the perimeter of the border plus the picture is 52.
Step-by-Step Calculation
Let the width of the border be w inches.
The length of the entire picture including the border is 8 + 2w inches (since there is a border on each side).
The width of the entire picture including the border is 10 + 2w inches.
Calculate the perimeter: P = 2(length + width) which is 2((8 + 2w) + (10 + 2w)) = 52.
Simplify the equation: 36 + 8w = 52.
Subtract 36 from both sides: 8w = 16.
Divide by 8: w = 2 inches.
Therefore, the width of the border is 2 inches.