Question

A picture that measures 8 x 10 has a border of uniform width surrounding it. the perimeter around the border is 52. find the width

A) 1 unit
B) 2 units
C) 3 units
D) 4 units
E) 5 units

Answer 1

The width of the border surrounding the 8 x 10 picture, which results in a total perimeter of 52 units, is calculated to be 2 units.

Step-by-step explanation:

The problem states that we have a picture measuring 8 x 10 units with a uniform border around it. The perimeter including the border is 52 units. To find the width of the border, we set up an equation taking into account the width of the border on all sides. Let's denote the width of the border as w. The dimensions of the picture including the border become (8+2w) by (10+2w).

We know that perimeter = 2 × length + 2 × width. Substituting in our known values gives us 52 = 2(8+2w) + 2(10+2w). Simplifying the equation results in 52 = 16 + 4w + 20 + 4w, which further simplifies to 52 = 36 + 8w. Solving for w, we get 16 = 8w, and w = 2.

Therefore, the width of the border is 2 units.