Question 632899
The perimeter of any polygon is calculated by adding the lengths of all the sides.
 
24. Since a rectangle has two pairs of congruent sides, two sides will have a length L, and the other two sides will have a length W, for a perimeter
{{{P=2L+2W}}} or {{{highlight(P=2(L+W))}}}
In this case {{{L+W=x+3x-8=4x-8}}} and {{{P=2(4x-8)}}} --> {{{highlight(P=8x-16)}}}
 
25. An equilateral triangle has three congruent sides, so if the length of each side is S, the perimeter, P, is
{{{P=3S}}}
If the length of each side is {{{S=2x}}}, the perimeter is
{{{P=3(2x)}}} --> {{{P=3*2*x}}} --> {{{highlight(P=6x)}}}
 
26.
a. If we  presume that the perimeters of the rectangle in problem 24 and the triangle in problem 25 are equal,
{{{8x-16=6x}}} --> {{{8x-6x-16=6x-6x}}} --> {{{2x-16=0}}} --> {{{2x-16+16=0+16}}} --> {{{2x=16}}} --> {{{2x/2=16/2}}} -->  {{{highlight(x=8)}}}
b.Substituting {{{x=8}}}, the perimeter for the rectangle is
{{{P=8x-16}}} --> {{{P=8*8-16}}} --> {{{P=64-16}}} --> {{{highlight(P=48)}}}
Substituting {{{x=8}}}, the perimeter for the triangle is
{{{P=6x}}} --> {{{P=6*8}}} --> {{{highlight(P=48)}}}