Respuesta :
Given the width of a rectangle = w
And the length given is [tex] \frac{3}{2} [/tex] units greater than its width.
So the length of the triangle = [tex] (w+\frac{3}{2}) [/tex]
We know that the perimeter of the rectangle is [tex] 2(length +width) [/tex]
So by plugging in the values of length and width in terms of w, we will get,
Perimeter = [tex] 2((w+\frac{3}{2})+w) [/tex]
= [tex] 2(w+\frac{3}{2}+w) [/tex]
We will add the like terms now.
[tex] 2(2w+\frac{3}{2} ) [/tex]
Now we have to expand this expression by distributing 2, We will get,
[tex] 4w+(\frac{3}{2} )(2) [/tex]
[tex] 4w+\frac{(3)(2)}{2} [/tex]
[tex] 4w+\frac{6}{2} [/tex]
[tex] 4w+3 [/tex]
So we have got the required perimeter of the rectangle in terms of w.
The perimeter is (4w+3) units.
