A rectangular picture has a length that is twice its width. The picture has an area of 162 square inches. Fidn the dimensions of the picture.
width --- x
length --- 2x
x(2x) = 162
x^2 = 81
what do you think?
To find the dimensions of the picture, we will use the information given in the problem.
Let's assume the width of the picture is "x" inches.
According to the problem, the length of the picture is twice its width, so the length would be 2x inches.
The formula for the area of a rectangle is length * width. In this case, the area is given as 162 square inches.
Using this information, we can set up the equation:
Area = Length * Width
162 = 2x * x
Now we will solve this equation:
2x^2 = 162
Divide both sides of the equation by 2:
x^2 = 81
To solve for x, take the square root of both sides:
x = √81
There are two possible solutions for x: x = 9 and x = -9. However, since a length or width cannot be negative, we discard the negative solution.
Therefore, the width of the picture is 9 inches.
Substituting this value back into the equation for the length:
Length = 2x = 2 * 9 = 18 inches
So, the dimensions of the picture are 18 inches by 9 inches.