Question

The length of a rectangle is 9 centimeters less than its width. what are the rectangles dimension if its area is 90.

Length of rectangle in cm:

Width of rectangle in cm:

Answer 1

Let the width of the rectangle be "X". Then the length of the rectangle will be (X-9).

Formula to find the area of a rectangle is given by-

`\small \underline{ \boxed{ \sf{ \pmb{Area_((rectangle)) = Length* Width }}}}\\`

On substituting the values-

`\:\:\:\:\:\:\longrightarrow \sf {Area_((rectangle)) = X * \bigg(X-9\bigg)}\\`

`\:\:\:\:\:\:\longrightarrow \sf {90 = X^2 -9X}\\`

`\:\:\:\:\:\:\longrightarrow \sf {X^2-9X =90}\\`

`\:\:\:\:\:\:\longrightarrow \sf {X^2-9X -90=0}\\`

`\:\:\:\:\:\:\longrightarrow \sf {X^2-15X+6X -90=0}\\`

`\:\:\:\:\:\:\longrightarrow \sf {X\bigg(X-15\bigg) +6* \bigg(X-15\bigg)=0}\\`

`\:\:\:\:\:\:\longrightarrow \sf {\bigg(X-15\bigg) * \bigg(X+6\bigg) =0}\\`

`\:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \red{X = 15\: Or,\: -6}}}}\\`

Since,width cannot be (Negative) , so the width will be 15cm.And the length will be (X-9)= (15-9)=6cm.