ANSWER
[tex]DA = 4inches[/tex]
EXPLANATION
The perimeter of a parallelogram is given by the formula,
[tex]perimeter = 2w + 2l[/tex]
It is the same as that of the rectangle.
We were given that the perimeter is 46 inches. So now we need to determine the length of the parallelogram using the equation
[tex]8 x - 5 = 3x + 10[/tex]
The reason is that, the opposite sides of a parallelogram are equal.
We solve the equation for x to obtain,
[tex]8x - 3x = 10 + 5[/tex]
This means that,
[tex]5x = 15[/tex]
Dividing through by 5, we obtain,
[tex]x = 3inches[/tex]
Meaning the length is
[tex]3(3) + 10 = 19inches[/tex]
We now plug in
[tex]l=19,perimeter=46[/tex]
into
[tex]perimeter = 2w + 2l[/tex]
to get,
[tex]46= 2w+ 2 \times 19[/tex]
[tex]46= 2w+ 38[/tex]
[tex]46 - 38= 2w[/tex]
[tex]8= 2w[/tex]
[tex]4= w[/tex]
DA is the width of the parallelogram, therefore
[tex]DA = 4inches[/tex]
