We will pick a distributive property. So, the situation is:
We have a frame with 2 colors black and white, we know that the width of the frame is 12 inches, the height of the black part is X inches and the height of the white part is 20 inches. Additionally, the area of the frame is 288 square inches.
The image represents the situation:
What is the height of the black part?
Now, we know that the area of the frame is equal to:
Area = width * height
Where height = 20 + X
So, replacing the values of the area and the width, we get:
288 = 12 * (20 + X)
Applying the distributive property:
288 = 12*20 + 12*X
288 = 240 + 12X
Solving for X:
288 - 240 = 12X
48 = 12X
48/12 = X
4 = X
Therefore, the height of the black part is 4 inches.