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.