Question

The border around a picture has the same width all the way around. The perimeter of the picture is 123 cm and the perimeter of the outside of the picture frame is 191 cm. Find an equation that can be used to find to find the width of the border around the picture?

Answer 1

2x +2y= 123, or

8a +2x +2y= 191

Explanation:

Perimeter of rectangle= 2(length) +2(width)

Let the length and the width of the picture be x and y respectively.

Perimeter of the picture= 2x +2y

2x +2y= 123 -----(1)

Let the width of the border be a.

Length of picture frame= a +x +a= 2a +x

Width of the picture frame= a +y +a= 2a +y

Outer perimeter of the frame= 191

2(2a +x) +2(2a +y)= 191

Expand:

4a +2x +4a +2y= 191

8a +2x +2y= 191 -----(2)

Substitute (1) into (2):

8a +123= 191

8a= 191 -123

8a= 68

a= 68 ÷8

a= 8.5 cm

Thus the width of the border is 8.5 cm.