11. If in the rhombus ABCD, AB -3x+4 and BC - 2x + 7, then find the length of DC and
AD
Answers
Answer:
Given that AB= 3x+2, BC = 4x+1, and CD= 5x-2, find the length of each side of parallelogram ABCD?
As opposite sides of a parallelogram are equal to each other, AB = CD and BC = AD. This means that 3x+2 = 5x-2.
3x+2+2 = 5x
2+2 = 5x-3x
4 = 2x
x = 4/2 = 2
Therefore, side AB is 3*2+2 = 8, same as CD (5*2–2 = 8)
BC IS 4x+1, and when we substitute the value of x, we get 4*2+1 = 8+1 = 9
Therefore, the final answer is that AB,CD are both 8 units long; BC and AD are both 9 units long.
You should make and label a sketch of the parallelogram. Since opposite sides of a parallelogram are congruent, side AB will have the same length as side CD. We can write and solve the equation 3x+2=5x-2. Once you've found the value of x, you can substitute into the expressions to find the lengths of each side. Side AD will of course be congruent to side BC.
AB=CD
3x+2=5x-2
2x=4
x=2
AB=3x+2
AB=3(2)+2
AB=8
BC=4x+1
BC=4(2)+1
BC=9
CD=5x-2
CD=5(2)-2
CD=8
BC=DA
DA=9