Question

A rectangle is drawn so that the width is 5 feet shorter than the length. The area of the rectangle is 50 square feet. Find the length of the rectangle.

feet

Answer 1

@dpasingh

Answer 2

let length = l
width = w
therefore according to the question we have

w= l-5
Area of rectangle = l*w

i.e. 50 = l(l-5)
i.e. \[\huge 50 = l^2 - 5l \rightarrow l^2- 5l -50 =0\]
\[\huge \rightarrow l^2- 10l +5l -50 =0\]
\[\huge \rightarrow l(l- 10) +5(l -10) =0\]
\[\huge \rightarrow l(l- 10) (l+5) =0\]
i.e. either l-10=0 or l+5 =0
i.e. l= 10
or \[\huge l =-5\]
we will take the positive value of l
hence length l of the rectangle is 10 feet

Answer 3

@cancherolugano

Answer 4

Sorry, remove l from the 7th line from down outside of the bracket

Answer 5

No problem thank you as always