Question

D
9.
In figure 11.21, one pair of adjacent sides of
a parallelogram is in the ratio 3:4. If one of
its angles, ZA is a right angle and diagonal
BD = 10 cm, find the-
3x
А AL
(i) lengths of the sides of the parallelogram.
4x
Fig. 11.21
(ii) perimeter of the parallelogram.​

Answer 1

Answer:

REF.image.

Given:In □ABCD

AB=DCandAD=BC

To prove: ABCD is a parallelogram

Construction: Draw diagonal AC and DB.

Proof: in △ABC and △ADC

AD=BC [Given]

AB=DC [Given]

AC=AC [Common side]

∴ By SSS property

△ADC≅△ACB

∴∠DAC=∠DCA

∴AB∣∣DC [By theorem]

In△ABDand△DCB

DB=DB [Common side]

AD=BC [Given]

AB=DC [Given]

∴△ABD≅△DCB

∴AD∣∣BC

Since AB∣∣DC and AD∣∣BC.

△ABCD is parallelogram