by definition, a rectangle has 90° angles so you can use the Pythagorean Theorem
width (w) = w
Length (L) = 4w - 5
Diagonal (D) = L + 10 = (4w - 5) + 10 = 4w + 5
w² + L² = D²
w² + (4w - 5)² = (4w + 5)²
w² + (16w² - 40w + 25) = (16w² + 40w + 25) expanded the squares
w² - 40w = 40w subtracted 16w² and 25 from both sides
w² - 80w = 0 subtracted 40w from both sides
w(w - 80) = 0 factored the equation
w = 0, w - 80 = 0 Zero Product Property staes to set each equal to 0
w = 0, w = 80 solved each equation
w = 80 eliminated w = 0 ... width must have a dimension!
Length (L) = 4w - 5 = 4(80) - 5 = 320 - 5 = 315
Diagonal (D) = L + 10 = (315) + 10 = 325
Answer: width=80, Length=315, Diagonal=325