The length of a rectangle is 4 inches greater than the width
Let the width = x
as length of a rectangle is 4 inches greater than the width
Length of rectangle = 4 + Width
Length =4 + x
Thus, the original measurements are :
Length = x + 4 and width = x
Area of the original rectangle = x(X + 4)
If each dimension is increased by 3 inches, the new area will be 99. square inches larger.
New dimension = 3 + Original dimenstion
New length = x + 4 + 3 = x + 7
New width =x + 3
Area of new rectangle = (x+3)(x+7)
as the new area will be 99. square inches larger.
i.e. New area = 99 + Original area
New area = 99 + x(x+4)
(x+3)(x+7)=99+x(x+4)
Simplify the expression for x :
[tex]\begin{gathered} (x+3)(x+7)=99+x(x+4)_{} \\ x^2+10x+21=99+x^2+4x \\ 10x-4x=99-21 \\ 6x=78 \\ x=\frac{78}{6} \\ x=13 \end{gathered}[/tex]x = 13
so, width = 13cm and for length :4 + x
Length = 13 + 4
Length = 17cm
Length = 17cm and width = 13cm
Answer : Dimension of original rectangle :Length = 17cm and width 13cm