Step-by-step explanation:
Assuming that the shape is a rectangle:
The area of a rectangle can be found with the following:
[tex]A = lw[/tex]
where [tex]l[/tex] is the length of the rectangle and [tex]w[/tex] is the width of the rectangle.
From the problem statement, we know that one side of the rectangle is [tex]4[/tex] and the other side is [tex]5x+ 7[/tex], and the rectangle has an area of [tex]128[/tex], so we can plug these values into the above formula to solve for [tex]x[/tex]:
[tex]128 = (4)(5x + 7)[/tex]
[tex]128 = 20x + 28[/tex]
[tex]20x = 100[/tex]
[tex]x = 5[/tex]
This means that the side lengths of the rectangle are [tex]4[/tex] and [tex]32[/tex] (plugging [tex]x = 5[/tex] back into the original side length).
The perimeter of a rectangle can be found with the following:
[tex]P = 2l + 2w[/tex]
Plugging in the values we have previously, we'll get the following:
[tex]P = 2(4) + 2(32)[/tex]
[tex]P = 8 + 64[/tex]
[tex]P = 72[/tex]
