Question 552071
the length of the wire is set equal to z.
the width of the rectangle is set equal to x.
the length of the rectangle is set equal to y.
the perimeter of the rectangle is equal to z.
the perimeter of the rectangle is also equal to 2x + 2y.
this results in:
2x + 2y = z
since z is the perimeter of the triangle also, then each side of the equilateral triangle is equal to z/3.
you have one equation in 3 unknowns which means that:
if you know the value of 2 of the unknowns, you can solve for the third value.
other than that, all you have is a relationship that will not yield a specific value unless you know 2 of the other values.
suppose we know that:
x = 5 and z = 60
we'll use the equation of 2x + 2y = z to get:
2(5) + 2y = 60
simplify this to get:
10 + 2y = 60
subtract 10 from both sides of this equation to get:
2y = 50
divide both sides of this equation by 2 to get:
y = 25
we now have:
x = 5 (given)
y = 25 (solved for)
z = 60 (given)
the dimensions of the rectangle are:
length = 5 and width = 25
the perimeter of the rectangle is equal to 2*5 + 2*25 which is equal to 60 which is the value of z.
the same value of z is also the perimeter of the triangle.
the length of each side of the triangle is set equal to k.
since the triangle is equilateral, then the length of each side of the triangle is equal to z/3 which makes k = z/3 which makes k equal to 60/3 which is equal to 20.
you have:.
the length of the rectangle is equal to x which is equal to 5
the width of the rectangle is equal to y which is equal to 25
the length of each side of the triangle is equal to k which is equal to 20.
the relationship between these is:
2x + 2y = 3k
this stems from 2*x + 2*y = z where z is equal to 3 * k where k is the length of each side of the triangle.
the equation of:
2x + 2y = z becomes:
2x + 2y = 3k
if you know 2 of the values, you can solve for the third.