Question

full explanation needed

the perimeter of a square is 56 metres. the area of a rectangle is 8 square metre less than the area of the given square if the length of the rectangle is 16 find its breadth.

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Answer 1

$\mathfrak{\huge{\green{\underline{\underline{ANSWER :}}}}}$

Hey there!!

The perimeter of square = ( 4 ) ( side )

( 4 ) ( side ) = 56

side = 56 ÷ 4

side = 14 m

The area of the of the rectangle is 8m² less than the area of the square

Area of the square = ( side )²

Area = ( 14 )²

Area = 196 m²

Now, the area of the rectangle = ( length ) × ( breadth )

Area = 196 - 8

Are = 188 m²

( length ) × ( breadth ) = 188 m²

Length = 16

( 16 ) × ( breadth ) = 188

Breadth = 188 ÷ 16

Breadth = 11.75 m

❤️Hope It Will Help You.❤️

Answer 2

$\huge\bf\underline \purple{Solution:-}$

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$\tt{Let ~the~ side~ of ~square~ be ~=~a}$

$\tt{perimeter~of ~square~=~4a}$

$\tt{Given~ perimeter~=~56m}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\tt{4a~=~56}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\tt\pink{a~=~56~÷~4~=~14m}$

⠀

$\tt{Area ~of ~square~=~{(14m)}^{2}~=~196sq.m}$

$\tt{Area~of~rectangle~=~Area~of ~square~-~8}$

⠀⠀⠀⠀⠀⠀⠀⠀$\tt\blue{=~196~-~8~=~188sq.m}$

⠀

$\tt{Let ~the ~length~ of~ rectangle~ be~ 'l'~ and~ breadth~ be~ 'b'}$

$\tt{Given~ length~=~16m}$

$\tt{Area~ of ~rectangle~=~l~×~b~=~188}$

$\tt{16b~=~188}$

$\tt{b~=~{\dfrac{188}{16}}}$

$\tt{b~=~{\dfrac{47}{4}}m}$

⠀

$\tt\red{Breadth~ of ~rectangle~=~{\dfrac{47}{4}}m~=~11.75}$

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