If DE=x+y, EC=12, CK=2x-y, and KD=3x-2y, then x=?, y=?, and the perimeter of DECK=?

Question

Quad. DECK is a parallelogram. Complete.

Answer 1

The key is to draw the parallelogram. Side 1 DE = x+y, Side 2 EC = 12, Side 3 CK = 2x-y, Side 4 KD = 3x-2y.

The definition of the parallelogram: opposite sides are equal. Therefore

Side 1 = Side 3; x+y=2x-y; simplify 2y=x

Side 2 = Side 4; 3x-2y = 12

Two equations, two unknown solve

3(2y)-2y = 12; 4y =12; y = 3

Then 2(3)=x; x=6

Solve for each side to get the perimeter

P = DE+EC+CK+KD = (3+6)+12+(2*6-3)+(3*6-2*3)=42