3.In kite ABCD lineAB congrent lineAD lineBC congrent lineDC AB = 6x + 5 ,AD = 3x + 3, and BC = x - 2. Find the perimeter (sum of lengths of all sides) of kite ABCD.

Answer 1

Give:

AB = 6x + 5

AD = 3x + 3

BC = x - 2

Line segment BC is congruent Line segment DC,

Then CD=BC = x - 2

Perimeter of the kite of ABCD equals to AB + AD + BC + CD:

Then,

p = 6x + 5 + 3x + 3 + x - 2 + x - 2

simplify:

p = 11x + 4

Answer 2

Since lineAB and lineAD are congruent, their lengths are equal. Since lineBC and lineDC are congruent, their lengths are equal.

Set AB equal to AD to solve for x:

AB = AD

6x + 5 = 3x + 3

3x = -2

x = -2/3

Now plug in x into each equation to find the length of each line:

AB = 6x + 5 = 6(-2/3) + 5 = 1

AD = 3x + 3 = 3(-2/3) + 3 = 1

BC = x - 2 = (-2/3) - 2 = -8/3

DC = BC = -8/3

Add all four lengths to find the perimeter of the kite:

P = AB + AD + BC + DC = 1 + 1 + (-8/3) + (-8/3) = -10/3

The only issue is that a length should never be negative. Are you sure those are the correct equations?