Question

The length of a rectangle is 5 m longer than twice the breadth. if the perimeter of the rectangle is 310m, find length and breadth.​

Answer 1

ᴛʜᴇ ʙʀᴇᴀᴅᴛʜ ᴏғ ᴀ ʀᴇᴄᴛᴀɴɢʟᴇ ʙᴇ x ᴄᴍ.

ᴛʜᴇʀᴇғᴏʀᴇ, ʟᴇɴɢᴛʜ ᴡɪʟʟ ʙᴇ 2x−5 ᴄᴍ.

ɴᴏᴡ, ʟᴇɴɢᴛʜ ɪs ᴅᴇᴄʀᴇᴀsᴇᴅ ʙʏ 5 ᴄᴍ ɪ.ᴇ., 2x−5−5=2x−10 ᴄᴍ ᴀɴᴅ ʙʀᴇᴀᴅᴛʜ ɪs ɪɴᴄʀᴇᴀsᴇᴅ ʙʏ 2 ᴄᴍ, ɪ.ᴇ., x+2 ᴄᴍ.

ᴀʟsᴏ ɢɪᴠᴇɴ, ᴘᴇʀɪᴍᴇᴛᴇʀ =74=2(ʟ+ʙ) ᴄᴍ.

ᴛʜᴇʀᴇғᴏʀᴇ, 2[2x−10+x+2]=74

⇒2[3x−8]=74

⇒6x−16=74

⇒6x=74+16

⇒6x=90

⇒x=15

ɴᴏᴡ, ʟᴇɴɢᴛʜ ᴡɪʟʟ ʙᴇ =2x−5=2(15)−5=30−5=25 ᴄᴍ.

ᴛʜᴇʀᴇғᴏʀᴇ, ʟᴇɴɢᴛʜ ᴀɴᴅ ʙʀᴇᴀᴅᴛʜ ᴏғ ᴀ ʀᴇᴄᴛᴀɴɢʟᴇ ᴀʀᴇ 25 ᴄᴍ ᴀɴᴅ 15 ᴄᴍ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ.

Answer 2

• Length of rectangle is 105 m.
• Breadth of rectangle is 50 m.

Explanation:

Given:-

• Perimeter of rectangle is 310 m.

To find:-

• Length and Breadth of rectangle.

Solution:-

Let, Breadth of rectangle be x m.

And, Length of rectangle be 2x + 5 m. [We take length be 2x + 5 because it is given that length is 5 m longer than twice the breadth]

Perimeter of rectangle = 2(Length × Breadth)

$\longrightarrow$ 310 = 2(2x + 5 + x)

$\longrightarrow$ 310 = 4x + 10 + 2x

$\longrightarrow$ 310 = 6x + 10

$\longrightarrow$ 310 - 10 = 6x

$\longrightarrow$ 300 = 6x

$\longrightarrow$ x = 300/6

$\longrightarrow$ x = 50

Verification:-

$\longrightarrow$ 310 = 2(2x + 5 + x)

• Put x = 50

$\longrightarrow$ 310 = 2×(2×50 + 5 + 50)

$\longrightarrow$ 310 = 2×(100 + 5 + 50)

$\longrightarrow$ 310 = 2×(105 + 50)

$\longrightarrow$ 310 = 210 + 100

$\longrightarrow$ 310 = 310

$\boxed{\sf Hence \: Verified.}$

We take

Length be 2x + 5 = 2×50 + 5 = 105 m.

Breadth be x = 50 m.