Question

In the below figure ABCD is a parallelogarm , DL is pependicular to ABand DM is perpendicular to BC . If AB = 18 cm, BC=12 cm and DM = 9.3cm, find DL .

Answer 1

$\bf{Given}$ :- ABCD is a parallelogram
AB =18 cm
BC = 12 cm
DM =9.3 cm


$\bf{To\:find}$:-DL=?

$\bf{Solution}$ :-

DL is perpendicular to AB.

So, Area of parallelogram ABCD = base × Height

=AB×DL

= 18×DL----(1)

DM is perpendicular to BC.

Area of parallelogram ABCD= base×height

=BC×DM

= 12×9.3

= 111.6 cm^2 -----(2)

Since in both equation 1 and 2 , the same thing is calculated ie area, so from equation 1 and 2

111.6 =18×DL

111.6/18=DL

$\boxed{\bf{6.2\: = DL}}$

Answer 2

$\mathcal{Given:}$
DL is perpendicular to AB
DM is perpendicular to BC
AB = 18 cm
BC = 12 cm
DM = 9.3 cm

$\mathcal{To find:}$
DL=?

$\mathcal{Solution:}$

DL is perpendicular to AB.

Area of parallelogram ABCD = Base × Height

= AB × DL

= 18 × DL -----(1)


DM is perpendicular to BC.

Area of parallelogram ABCD = Base × Height

= BC × DM

= 12 × 9.3

= 111.6 cm -----(2)


Since, both (1) and (2) are areas of parallelogram ABCD,

Equation 1 = Equation 2

Therefore,

18 × DL = 111.6

DL = 111.6/18

So,

$\boxed{DL = 6.2 cm}$