Respuesta :
Given :
- The length of a rectangle is 2 cm less than its width.
- Area of the rectangle is 168 cm²
To Find :
- The dimensions of the rectangle.
Solution :
- Let us assume the length of the rectangle as x cm and therefore the breadth will be (x + 2) cm
We know that,
[tex] \purple{ \boxed{\quad \bf Length \times Width = Area_{(rectangle)}}}[/tex]
Now, Putting the values in the formula :
[tex]{ \qquad \sf { \dashrightarrow{ x(x + 2)= 168 {cm}^{2} }}}[/tex]
[tex]{ \qquad \sf { \dashrightarrow{ {x}^{2} + 2x= 168 }}}[/tex]
[tex]{ \qquad \sf { \dashrightarrow{ {x}^{2} + 2x - 168=0 }}}[/tex]
[tex]{ \qquad \sf { \dashrightarrow{ {x}^{2} - 12x + 14x - 168 = 0 }}}[/tex]
[tex]{ \qquad \sf { \dashrightarrow{ {x}(x - 12) + 14(x - 12) = 0 }}}[/tex]
[tex]{ \qquad \sf { \dashrightarrow{ ({x}+ 14)(x - 12) = 0 }}}[/tex]
[tex]{ \qquad \sf { \dashrightarrow{ ({x}+ 14) = 0 }}}[/tex]
[tex]{ \qquad \sf { \dashrightarrow{ {x}= - 14 }}}[/tex]
[tex]{ \qquad \sf { \dashrightarrow{ ({x} - 12) = 0 }}}[/tex]
[tex]{ \qquad \sf { \dashrightarrow{ {x} = 12 }}}[/tex]
- Whether x = (–14) or 12
The length of the rectangle can never be negative so the length must be 12 cm .
Therefore, Width = (12 + 2) = 14 cm .
