Question

A square and a rectangular field with measurements as given in the figure have the same
perimeter. Which field has a larger area?
​

Answer 1

Answer:

(A) is larger area

$\bold\red{ Step \: by \:step\: Explanation :-\: }$

Perimeter of figure (a) = 4 × side = 4 × 60 = 240m

Perimeter of figure (b) = 2 [l + b]

Perimeter of figure (b) = Perimeter of figure (a)

2[l + b] = 240

⇒ 2 [80 + b] = 240

⇒ 80+ b = 120

⇒ b = 120– 80 = 40 m

Area of figure (A) = (side)2 = 60 × 60 = 3600 m2

Area of figure (B) = l × b = 80 × 40 = 3200 m2

So, area of figure (A) is Longer than the Area of figure (B).

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Answer 2

αղsաҽɾ:

ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏғ ғɪɢᴜʀᴇ (ᴀ) = 4 × sɪᴅᴇ = 4 × 60 = 240ᴍ

ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏғ ғɪɢᴜʀᴇ (ʙ) = 2 [ʟ + ʙ]

ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏғ ғɪɢᴜʀᴇ (ʙ) = ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏғ ғɪɢᴜʀᴇ (ᴀ)

2[ʟ + ʙ] = 240

⇒ 2 [80 + ʙ] = 240

⇒ 80+ ʙ = 120

⇒ ʙ = 120– 80 = 40 ᴍ

ᴀʀᴇᴀ ᴏғ ғɪɢᴜʀᴇ (ᴀ) = (sɪᴅᴇ)2 = 60 × 60 = 3600 ᴍ2

ᴀʀᴇᴀ ᴏғ ғɪɢᴜʀᴇ (ʙ) = ʟ × ʙ = 80 × 40 = 3200 ᴍ2

sᴏ, ᴀʀᴇᴀ ᴏғ ғɪɢᴜʀᴇ (ᴀ) ɪs ʟᴏɴɢᴇʀ ᴛʜᴀɴ ᴛʜᴇ ᴀʀᴇᴀ ᴏғ ғɪɢᴜʀᴇ (ʙ).

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