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