Question

answer the above question give step vise explainetion​

Answer 1

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } GiveN:-}}}}}$

• ❒ A rectangular playground has an area of 420m².
• ❒ Its lenght is increased by 7m.
• ❒ Its breadth is decreased by 5m.

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } To\:FinD:-}}}}}$

• ❒ The length and breadth of playground.

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } FormulA\:UseD:-}}}}}$

$\tt We \:can\:found\:area\:as$

$\large\orange{\underline{\boxed{\purple{\bf{\dag Area\:\:=\:\:lenght\:\times\:breadth }}}}}$

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } AnsweR:-}}}}}$

Here we will have two cases ,

$\underline{\green{\tt \mapsto Case\:\:1:-}}$

$\sf Let\:us\:take\:the$

• ➳ Length be x .
• ➳ Breadth be y .

$\tt:\implies Area=length\times breadth$

$\tt:\implies Area=x\times y$

$\underline{\boxed{\red{\tt{\longmapsto \:\:xy\:\:=\:\:420m^2\:\:}}}}$

________________________________________

$\underline{\green{\tt \mapsto Case\:\:2:-}}$

$\sf Let\:us\:take\:the$

• ➳ Length be ( x + 7 ) m .
• ➳ Breadth be ( y - 5 ) m.

$\tt:\implies Area=length\times breadth$

$\tt:\implies Area=(x+7)\times( y-5)$

$\tt:\implies 420m^2=x(y-5)+7(y-5)$

$\tt:\implies xy - 5x + 7y - 35 = 420m^2$

$\tt:\implies \bigg( x\times \dfrac{420}{x}\bigg)-5x+\bigg(7\times\dfrac{420}{x}\bigg)-35=420$

$\tt:\implies \cancel{420}-5x+\dfrac{2940}{x}-35=\cancel{420}$

$\tt:\implies -5x^2+2940-35x=0$

$\tt:\implies 5x^2+35x-2940=0$

$\tt:\implies 5(x^2+7x-588)=0$

$\tt:\implies x^2+7x-588=0$

$\tt:\implies x^2+28x-21x-588=0$

$\tt:\implies x(x+28)-21(x+28)=0$

$\tt:\implies (x-21)(x+28)=0$

$\tt:\implies x = 21,(-28)$

$\tt Neglecting\: negative\:value\:since\:sides$

$\tt cannot\:be\; negative.$

$\underline{\boxed{\red{\tt{\longmapsto \:\:x\:\:=\:\:21\:\:}}}}$

$\blue{\bf Hence\: length\:and\: breadth\:are :}$

• $\green{\boxed{\orange{\tt Length\:\:=\:\:x\:=\:\pink{21m}}}}$

• $\green{\boxed{\orange{\tt Breadth\:\:=\:\:\dfrac{420}{x}\:=\:\bigg(\dfrac{\cancel{420m}}{\cancel{21m}}\bigg)\:=\:\pink{20m}}}}$