Question

in parallelogram ABCD, AB=12 cm altitude DM and DN correspondence to base AB and BC respectively. if DM=5 and DN=6 then find the length of bc​

Answer 1

Answer:

BC = 10 cm

Step-by-step explanation:

In a parallelogram, opposite sides are equal. So AB = CD = 12cm

Draw a diagonal DB.

Area of triangle ABD = 0.5 X Base x Height = 0.5 x 12 x 5 = 30 sq. cm.

Area of triangle DBC = 30 sq. cm too as both triangles are congruent.

30 = 0.5 x BC x DN  = 0.5 x BC x 6

30 = 3 x BC

So BC = 30 / 3 = 10 cm

Ans: BC= 10 cm

Answer 2

The length of BC is 10 cm.

Step-by-step explanation:

Given:

ABCD is a Parallelogram,

AB = 12 cm

DM = 5 cm

DN = 6 cm

To Find:

BC = ?

Solution:

Area of Parallelogram is given as

$\textrm{Area of Parallelogram}=Base\times Height$

For Parallelogram ABCD when

Base = AB = 12 cm

Height = DM = 5 cm

$\textrm{Area of Parallelogram}=12\times 5=60\ cm^{2}$

Now,

For Parallelogram ABCD when

Base = BC = ?

Height = DN = 6 cm

Area will remain Same as same Parallelogram,

$\textrm{Area of Parallelogram}=BC\times 6\\\\BC=\dfrac{60}{6}=10\ cm$

Therefore,

The length of BC is 10 cm.