Question

1.
The given figure shows parallelogram ABCD. Diagonals AC
and BD of the parallelogram intersect at point O.
If OD = (6x + 4) cm, BO = (8x - 16) cm, OC = (6y + 17) cm and
AO = (8y + 1) cm, then find the perimeter of ABOC.
a. 150 cm
b. 165 cm
c. 2(4x + 3y)
d. 180 cm
36 cm
D
54cm
C​

Answer 1

Answer:

figure shows parallelogram ABCD. Diagonals AC

and BD of the parallelogram intersect at point O.

If OD = (6x + 4) cm, BO = (8x - 16) cm, OC = (6y + 17) cm and

AO = (8y + 1) cm, then find the perimeter of ABOC.

a. 150 cm

b. 165 cm

c. 2(4x + 3y)

d. 180 cm

36 cm

D

54cm

C

Answer 2

Let us look at the answer:

Step-by-step explanation:

The diagonals of a parallelogram bisect each other

⇒   OB=OD  ⇒ 6x+4 = 8x-16 ⇒ 6x-8x = -16-4 ⇒ -2x = -20 ⇒x = 10

Also,  OA= OC ⇒ 8y+1 = 6y+17  ⇒ 2y= 16 ⇒ y = 8

⇒ AC = OA+ OC = 8y+1+6y+17 = 14y+18 = 14×8 +18 = 112+18 = 130 cm  

it is given that the two sides of ΔABC, AB= 36 cm and BC = 54 cm

So the perimeter of ΔABC = AB+BC +AC  = 36+54 +130 = 220 cm