The mat and frame around the picture shown measures $x$ inches across. Which equation says that the area of the picture itself is $700 \mathrm{in}^{2}$ ?
Choose the correct answer below.
A. $(40-2 x)(19-2 x)=700$
B. $2(40-2 x)+2(19-2 x)=700$
C. $x(40)(19)=700$
D. $(40-x)(19-x)=700$

Step 1 ：The area of a rectangle is given by the formula length * width. In this case, the length and width of the picture (not including the mat and frame) would be \((40-2x)\) and \((19-2x)\) respectively, because we subtract the width of the mat and frame (which is x on each side) from the total length and width.

Step 2 ：Therefore, the equation that represents the area of the picture itself being 700 square inches would be \((40-2x)(19-2x) = 700\).

Step 3 ：Solving this equation gives us two possible solutions for x: \(\frac{59}{4} - \frac{\sqrt{3241}}{4}\) and \(\frac{\sqrt{3241}}{4} + \frac{59}{4}\).

Step 4 ：Final Answer: The correct answer is \(\boxed{\text{(A) } (40-2x)(19-2x) = 700}\).