A rectangular picture has a length that is twice its width. The picture has an area of 12 square inches. Find the dimensions of the picture.
L = 2 W
L * W = 12
substituting ... 2 W * W = 12 ... W^2 = 6
solve for W , substitute back to find L
To find the dimensions of the picture, we need to set up an equation based on the given information.
Let's assume the width of the picture is "w" inches.
Since the length is twice the width, the length would be "2w" inches.
The area of a rectangle is given by the formula: Area = Length * Width.
Based on the given information, we know the area of the picture is 12 square inches. So, we can write the equation as:
12 = (2w) * w
Now, we can solve this equation to find the dimensions of the picture.
First, simplify the equation:
12 = 2w^2
Divide both sides of the equation by 2:
6 = w^2
Take the square root of both sides of the equation:
√6 = w
So, the width of the picture is approximately √6 inches.
To find the length, we can substitute the value of the width back into the equation:
Length = 2w = 2 * √6
Therefore, the dimensions of the picture are approximately √6 inches for the width and 2 * √6 inches for the length.