Question

2) ABCD is a rectangle AB = 7cm.,
BC = 24 cm., OB = 12.5 cm.
ZABD = 35° find DC, AD, BD, AC
ZBDC and ZDBC​

Answer 1

Answer:

use identity to factorise

Answer 2

Given :- ABCD is a rectangle AB = 7cm., BC = 24 cm., OB = 12.5 cm. ∠ABD = 35° .

To Find :-

• DC, AD, BD, AC ∠BDC and ∠DBC .

Solution :-

→ DC = AB = 7 cm. (Ans.) { Opposite sides of a rectangle are equal.}

→ AD = BC = 24 cm. (Ans.) { Opposite sides of a rectangle are equal.}

now, since all angles of a rectangle are 90° .

in right angled ∆DCB,

→ DC² + BC² = BD² (using pythagoras)

→ 7² + 24² = BD²

→ 49 + 576 = BD²

→ BD² = 625

→ BD = √(625)

→ BD = 25 cm.

then,

→ BD = AC = 25 cm. (Ans.) { Diagonals of a rectangle are equal .}

now,

→ ∠BDC = ∠ABD { Alternate angles since AD || BC . }

→ ∠BDC = 35° (Ans.)

and,

→ ∠DBC = 90° - ∠ABD

→ ∠DBC = 90° - 35°

→ ∠DBC = 55° (Ans.)

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