the area of rectangle is 21 cm if one sides exceeds the other by 4 cm .find the dimensions of rectangle
Let the length of the shorter side be x cm. Then the length of the longer side would be x+4 cm.
The area of the rectangle is the product of the two sides:
Area = (x) * (x+4)
Since we know the area is 21 cm², we can set the equation equal to 21:
21 = x(x+4)
Now we can solve for x:
21 = x² + 4x
0 = x² + 4x - 21
Factoring the quadratic equation:
0 = (x - 3)(x + 7)
Setting each factor equal to zero and solving for x:
x - 3 = 0 => x = 3
x + 7 = 0 => x = -7
Since the side's length cannot be negative, we choose the positive value for x:
Shorter side (x): 3 cm
Longer side (x+4): 3 + 4 = 7 cm
The dimensions of the rectangle are 3 cm and 7 cm.