Question

The length of a rectangle is 2 centimeters less than its width. What are the dimensions of the rectangle if its area is 168 square centimeters

Answer 1

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,

`\purple{ \boxed{\quad \bf Length * Width = Area_((rectangle))}}`

Now, Putting the values in the formula :

`{ \qquad \sf { \dashrightarrow{ x(x + 2)= 168 {cm}^(2) }}}`

`{ \qquad \sf { \dashrightarrow{ {x}^(2) + 2x= 168 }}}`

`{ \qquad \sf { \dashrightarrow{ {x}^(2) + 2x - 168=0 }}}`

`{ \qquad \sf { \dashrightarrow{ {x}^(2) - 12x + 14x - 168 = 0 }}}`

`{ \qquad \sf { \dashrightarrow{ {x}(x - 12) + 14(x - 12) = 0 }}}`

`{ \qquad \sf { \dashrightarrow{ ({x}+ 14)(x - 12) = 0 }}}`

`{ \qquad \sf { \dashrightarrow{ ({x}+ 14) = 0 }}}`

`{ \qquad \sf { \dashrightarrow{ {x}= - 14 }}}`

`{ \qquad \sf { \dashrightarrow{ ({x} - 12) = 0 }}}`

`{ \qquad \sf { \dashrightarrow{ {x} = 12 }}}`

• 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 .