Question

ABCD is a rect. Find the following​

Answer 1

Step-by-step explanation:

ABCD a rectangular ..so each corner is 90° angle

....angle OBC= 45° because diagonal cut the angle in 45° .......angle ADO= 45° .......

angle AOB = 180 - ( 27+45) = 108° ...

angle OCB = 45° ....

angle AOD = 180 - (63° + 45° ) = 72° ......

Answer 2

$\huge\bf\red{ɢɪᴠᴇɴ :}$

ᴛʜᴇ ʙᴀꜱᴇ ᴏꜰ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ ɪꜱ ᴛʜʀɪᴄᴇ ɪᴛꜱ ʜᴇɪɢʜᴛ.

ᴀʀᴇᴀ ᴏꜰ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ = 867 ᴄᴍ²

$\huge\bf\red{Tᴏ Fɪɴᴅ :}$

ᴛʜᴇ ʜᴇɪɢʜᴛ.

ᴛʜᴇ ʙᴀꜱᴇ.

$\huge\bf\red{Sᴏʟᴜᴛɪᴏɴ : }$

ʜᴇɴᴄᴇ,ɪᴛ ɪꜱ ɢɪᴠᴇɴ ᴛʜᴀᴛ ᴛʜᴇ ʙᴀꜱᴇ ᴏꜰ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ ɪꜱ ᴛʜʀɪᴄᴇ ɪᴛꜱ ʜᴇɪɢʜᴛ.

ʟᴇᴛ'ꜱ ꜰɪʀꜱᴛ ᴄᴏɴꜱɪᴅᴇʀ ᴛʜᴇ ʜᴇɪɢʜᴛ ᴏꜰ ᴛʜᴇ ᴘᴀʀᴀʟʟᴇʟᴏɢʀᴀᴍ ʙᴇ x ᴛʜᴇɴ ᴛʜᴇ ʙᴀꜱᴇ ᴡɪʟʟ ʙᴇ 3×x = 3x

Now,

${\underline{\boxed{\sf{\blue{Area_{(parallelogram)}=base\times{height}}}}}}$

$\dashrightarrow\sf{867=3x\times{x}}$

$\dashrightarrow\sf{867=3x^2}$

$\dashrightarrow\dfrac{\cancel{867}^{289}}{\cancel{3}^1}\sf{=x^2}$

$\dashrightarrow\sf{289=x^2}$

$\dashrightarrow\sf{x=\sqrt{289}}$

$\dashrightarrow\sf{x=\sqrt{17\times{17}}}$

$\bigstar\underline{\boxed{\sf{\pink{x=17}}}}$

${\text{\sf{Therefore,the Height (x) is 17cm}}}$

${\text{\sf{And the Base (3x)}}}\sf{= 3\times{17}=51 cm.}$