Question

plz solve this........​

Answer 1

Solution :-

**Please refer diagram in the attachment.

We have :-

♦ ABCD is a parallelogram.

♦ ABE is a triangle.

♦ AB || DC and AD || BC ( ABCD is a parallelogram)

♦ AD = 18 cm

♦ ar. ∆ ABE = 5/6 ar. Parallelogram ABCD

Constructions :-

♦ EH perpendicular to AB ( or height)

♦ "G" point of intersection of EH at DC

♦ "F" point of intersection of EB at DC

Now by using properties of Triangle and Parallelogram :-

♦ ∠DAB = ∠BCF ( opposite angle of parallelogram)

♦ ∠BFC = ∠EFD ( vertically opposite)

♦ ∠DAB = ∠EDF ( corresponding angle)

♦ ∠ABE = ∠DFE ( corresponding angle)

Now in ∆DFE & ∆CFB

• ∠EDF = ∠BCF

• ∠EFD = ∠BFC

Therefore ∆EDF ≈ ∆BCF ( Via A-A )

Now in ∆ABE & ∆DFE

• ∠EAB = ∠EDF

• ∠AEB = ∠DEF ( common angle)

Therefore ∆ABE ≈ ∆DFE ( Via A-A )

♦ Ratio of Height = Ratio of sides

By using question :-

→ EH × 1/2 × AB = 5/6 × GH × AB

→ GH = 3/5 EH

Or

→ EG = 2/5 EH ( As EG + GH = EH)

Or

$\dfrac{EG}{EH} = \dfrac{2}{5}$

(a)

As ∆ABE ≈ ∆DFE

♦ Ratio of Height = Ratio of sides

$\implies \dfrac{EG}{EH} = \dfrac{ED}{EA} = \dfrac{2}{5}$

$\implies \dfrac{DA}{EA} = \dfrac{3}{5} \: (as \: EA = AD + DE )$

→ DA = 3/5 EA

→ 18 = 3/5 EA

→ EA = 30

or DE = 12 cm

(b)

Now Area of Parallelogram ABCD = 450 sq. cm

→ AD × Height from B = 450

→ 18 × Height from B = 450

→ Height from B = 450 ÷ 18

Height from B = 25 cm