Given -
➙ The length of a rectangle is 4 cm greater than its width.
- here if we let the length as l and width as b then according to the question l = b + 4 cm.
➙ If its area is 96cm². i.e A = 96cm²
To find -
➙ The length of the rectangle.
Solution -
As we know to find the area of rectangle we use the formula,
Area of rectangle (A) = Length of the rectangle (l) × Width of the rectangle (b)
Putting the values given in the question,
l × b = A
➠ (b + 4) × b = 96
➠ b² + 4b = 96
➠ b² + 4b - 96 = 0
By using the factorisation method we will find the value of b, breadth and then we will put it in the above formed equation to find the value of l, length.
➠ b² + 4b - 96 = 0
➠ b² + 12b - 8b - 96 = 0
➠ b(b + 12) - 8(b +12) = 0
➠ (b + 12)(b - 8) = 0
➠ b = 8, - 12
Here, we will consider 8 as the value of b because the breadth can never be in negative.
➠ l = b + 4
➠ l = 8 + 4
➠ l = 12
Therefore, the length of the rectangle is 12cm.