the width of a rectangular painting is 2 meters less than the length, the area of the painting is 20 M^2
L(L-2) = 20
To find the width and length of a rectangular painting, we can use the given information that the width is 2 meters less than the length, and the area of the painting is 20 square meters.
Let's assume the length of the painting is L meters. Therefore, the width would be L - 2 meters.
The formula for finding the area of a rectangle is: Area = Length × Width.
Given that the area is 20 square meters, we can substitute the values into the formula:
20 = L × (L - 2)
Now, let's solve this equation to find the value of L:
20 = L^2 - 2L
Rearranging the equation:
L^2 - 2L - 20 = 0
This is a quadratic equation, so let's factorize it:
(L - 5)(L + 4) = 0
Setting each factor equal to zero:
L - 5 = 0 or L + 4 = 0
Solving for L:
L = 5 or L = -4
Since length cannot be negative in this context, we can discard the second solution. Therefore, the length of the painting is 5 meters.
Substituting this value back into the equation for width:
Width = L - 2 = 5 - 2 = 3 meters
Hence, the length of the painting is 5 meters, and the width is 3 meters.