A rectangular picture is twice as long as it is wide and is to be mounted on a mat with the same proportion. If the picture is 18 inches wide, can it be
mounted on a mat of 259 square inches? To answer this, find the width of the mat.
L = 2W
L*W = 259
Substitute 2W for L in the second equation and solve for W.
To find the width of the mat, we need to first find the dimensions of the rectangular picture.
Given that the picture is twice as long as it is wide, and the width is 18 inches, we can calculate the length.
Length = 2 * Width
Length = 2 * 18 = 36 inches
Now, we need to find the area of the rectangular picture to see if it can be mounted on a mat of 259 square inches.
Area of a rectangle = Length * Width
Area of the picture = 36 * 18 = 648 square inches
Now, let's calculate the width of the mat.
Area of the mat = Width of the mat * Length of the mat
Since the picture and mat have the same proportional dimensions, we can set up the equation:
648 = Width of the mat * Length of the mat
We need to solve for the Width of the mat. But we know only the area of the mat, which is 259 square inches. So, let's rearrange the formula to solve for the Width of the mat.
259 = Width of the mat * Length of the mat
We know that the length of the mat is the same as the length of the picture, which is 36 inches.
259 = Width of the mat * 36
Now, we can solve for the Width of the mat by dividing both sides of the equation by 36.
259 / 36 = Width of the mat
Width of the mat ≈ 7.19 inches
Therefore, the width of the mat is approximately 7.19 inches.