how wide is the strip of the mat showing around the picture?

Question

al paints with watercolors on asheet of paper 26 inches wide by 18 inches high.he then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. the perimeter of the mat is 104 inches. how wide is the strip of the mat showing around the picture?

Answer 1

Hi Melyssa;

Perimeter=2(l+w)

104=2[(26+l)+(18+w)]

Because this is a "uniformly wide strip", the additional length and width are of equal value.  We will call such x.

104=2[(26+x)+(18+x)]

Combine like terms...

104=2(2x+44)

104=4x+88

Let's subtract 88 from both sides..

104-88=4x+88-88

16=4x

Let's divide both sides by 4...

16/4=(4x)/4

4=x

The width of the strip is 4 inches.

Answer 2

the strip is uniformly 4 inches wide. The full mat measures 22 inches wide and 30 inches high.