Question

5. In the given parallelogram ABCD, AL I BC and
CM I AB. If AL = 4 m, CM = 2 m and BC = 3 m,
find DC.
D
12
3
B.
M
ih
1
1
L​

Answer 1

Referring to the figure given, we have,
ABCD is a parallelogram and we know that the opposite facing sides of a parallelogram are equal ∴ AB = DC and BC = AD
AL is perpendicular to BC
MC is perpendicular to AB
AL = 4 m
CM = 2 m
BC = 3 m
We know that the formula of the area of a parallelogram is given by,
Area = Base × Altitude
Firstly, we have
Side BC = 3 m and the perpendicular height corresponding to this side, AL which is 4 m.
∴ Area = BC × AL = 3 × 4 = 12 m²
Now, considering the side AB, the corresponding altitude of this side, CM which is 2 m.
∴ Area = AB × CM
⇒ 12 = AB × 2
⇒ AB = 12/2
⇒ AB = 6 m
Since AB = DC
∴ DC = 6 m