Question

The perimeter of a rect. Is 104cm.The length of it is 3 times it’s breadth.Find the length of the rectangle

Answer 1

Given,



=>Perimeter of a rectangle is 104 cm



=>The length of the same rectangle is equal to thrice its breadth




To find,



The length and breadth of the same rectangle




Main solution :



Let the breadth of the rectangle be equal to x cm



So, according to question the length of this rectangle will be 3x



We know,



Perimeter of a rectangle=2(length+breadth)3x



Substituting the values,



2(3x + x ) = 104 cm



Solving for x using transposition



6x + 2x = 104 cm



8x = 104 cm



x = 13 cm





Therefore,



Breadth of the rectangle = x = 13cm



Length of the rectangle = 3x = 39 cm

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,

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

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

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

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

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

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

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

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

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

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