Answer:
Width=7.5 ft
Length=17.5 ft
Step-by-step explanation:
-Let w be the width's dimension.
-Therefore Length=w+10
-The area is given as 131.25 sq ft.
-We substitute in the area formula to solve for w:
[tex]Area=Length\times Width\\\\131.25=w(w+10)\\\\131.25=w^2+10w\\\\\#Equate \ to \ 0\\\\w^2+10w-131.25=0\\\\100w^2+1000w-13125=0\\\\w_1,w_2=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w_1,w_2=\frac{-1000\pm \sqrt{1000^2-4\times100\times(-13125}}{2\times100}\\\\w_1=7.5, w_2=-17.5\\\\\therefore w=w_1=7.5\ ft\\\\length=w+10=7.5+10=17.5\ ft[/tex]
Hence, the length of the rectangle is 17.5 ft and the width is 7.5 ft
