The length of rectangle is 31 yards and width is 24 yards.
Step-by-step explanation:
Given,
Width of rectangle = w
Length of rectangle = w+7
Area of rectangle = 744 square yards
Area = Length * width
[tex]744=w(w+7)\\744=w^2+7w\\0=w^2+7w-744\\w^2+7w-744=0[/tex]
Factorizing the equation
[tex]w^2+31w-24w-744=0\\w(w+31)-24(w+31)=0\\(w+31)(w-24)=0[/tex]
Either,
w+31=0, =>w= -31
Or,
w-24=0 =>w=24
As width cannot be negative, therefore,
Width = 24 yards
Length = w+7 = 24+7 = 31 yards
The length of rectangle is 31 yards and width is 24 yards.
Keywords: area, rectangle
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