If the perimeter is 101.76 in, we can create an equation of 2l + 2w = 101.76 in (length is l, and width is w). We also have that the rectangular painting is 5.82 in taller than it is wide. We can create a new equation stating that l = w + 5.82. We can now substitute l for w + 5.82 into our original equation, 2l + 2w = 101.76, and we get 2(w + 5.82) + 2w = 101.76. Now simplify and get 4w + 11.64 = 101.76. Simplifying this the whole way, we get w = 22.53. Now plug this value of w back into the equation, l = w + 5.82, and we get l = 22.53 + 5.82 = 28.35. We now have width: 22.53 in. and length: 28.35 in.
