Question

plzzzz solve it....​

Answer 1

${ \frak { \underline\purple{\qquad Given\: :\qquad}}} \:$

Length of playground is 2 m larger than it's width and it's area is 195m²

${ \frak { \underline\purple{\qquad To\:Find\: :\qquad}}} \:$

Length and width of the playground.

${ \frak { \underline\purple{\qquad Diagram \::\qquad}}} \:$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large x + 2 m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large x m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

${ \frak { \underline\purple{\qquad Solution\: :\qquad}}} \:$

$\:\:\:\:\:\:\bullet\:\sf{Let \:it's \:width(w)\: = x \:m}$

$\:\:\:\:\:\:\bullet\:\sf{\therefore\:Length(l)\: =\: x \:+ 2\: m}$

${\red\bigstar\:\underline{\boxed {\bold \green {Area_{(rectangle)}\:\leadsto\:width(w)\:\times\:length(l)}}}}$

Putting all values in the formulated :-

$\sf{x\:\times\:(x\:+\:2)\:=\:195}$

$\sf{x^2\:+\:2x\:=\:195}$

$\sf{x^2\:+\:2x\:=\:195}$

$\sf{x^2\:+\:2x\:-\:195\:=\:0}$

☯ Quadratic equation formed !! ☯

☯ Let's solve it !! ☯

$\sf{x^2\:+\:15x\:-\:13x\:-\:195\:=\:0}$

$\sf{x(x\:+\:15)\:-\:13(x\:+\:15)\:=\:0}$

$\sf{(x\:+\:15)\:(x\:-\:13)\:=\:0}$

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Value of x for , (x + 15) = 0

➱ x = 0 - 15

➱ x = -15

Value of x for , (x - 13) = 0

➱ x = 0 + 13

➱ x = 13

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☯ Width cannot be negative !! ☯

$\underline{\boxed {\bold {\therefore \purple {x\:=\:width(w)\:=\:13}}}}\:\pink\bigstar$

Length

➪ $\sf{ x \:+ \:2}$

➪ $\sf{13\:+\:2}$

➪ $\sf\underline{15}$

$\underline{\boxed {\bold {\therefore \orange {x\:+\:2\:=\:length(l)\:=\:15}}}}\:\green\bigstar$

${ \frak { \underline\purple{\qquad Note :\qquad}}} \:$

Dear user if you are not able to see the diagram from app. Please see it from the the site (brainly.in). It will be correctly displayed there.

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Answer 2

Area of the rectangular playground =195 m²

To find:

Length =?, Breadth =?

Solution:

Let breadth of the rectangular playground =b

Length of the rectangular playground =(b+2)

Area of rectangular playground = Length × Breadth

⇒195=(b+2)×b²

⇒195=b² +2b

⇒b²+2b−195=0

⇒b²+15b−13b−195=0

⇒b(b+15)−13(b+15)=0

⇒(b−13)(b+15)=0

⇒b=13 or b=−15

Value b of can't be negative. So b=13

Therefore, breadth of the rectangular playground =13 m

and length of the rectangular playground =15 m