Answer: The dimensions are: " 1.5 mi. × ³⁄₁₀ mi. " . _______________________________________________ { length = 1.5 mi. ; width = ³⁄₁₀ mi. } . ________________________________________________ Explanation: ___________________________________________ Area of a rectangle:
A = L * w ;
in which: A = Area = (9/20) mi.² , L = Length = ? w = width = (1/5)*L = (L/5) = ? ________________________________________ A = L * w ; we want to find the dimensions; that is, the values for "Length (L)" and "width (w)" ; _______________________________________ Plug in our given values: _______________________________________ (9/20) mi.² = L * (L/5) ; in which: "w = L/5" ;
→ (9/20) = (L/1) * (L/5) = (L*L)/(1*5) = L² / 5 ;
↔ L² / 5 = 9/20 ;
→ (L² * ? / 5 * ?) = 9/20 ?
→ 20÷5 = 4 ; so; L² *4 = 9 ;
↔ 4 L² = 9 ;
→ Divide EACH side of the equation by "4" ;
→ (4 L²) / 4 = 9/4 ; ______________________________________ to get: → L² = 9/4 ; Take the POSITIVE square root of each side of the equation; to isolate "L" on one side of the equation; and to solve for "L" ; ___________________________________________
