Question

solve the problem with explanation​

Answer 1

$\sf\large\underline\green{Let:-}$

$\sf{\implies The\: length\:_{(playground)}=x}$

$\sf{\implies The\: breadth\:_{(playground)}=y}$

$\sf\large\underline\green{Given:-}$

$\sf{\implies Area\:_{(playground)}=420\:m^2}$

$\sf\large\underline\green{To\: Find:-}$

$\sf{\implies The\: dimensions\:_{(playground)}=?}$

$\sf\large\underline\green{Solution:-}$

To calculate the dimensions of rectangular playground , at first we have to set up equation as per the given Question by applying formula. Then solve those equation after that you get the value of x and y where x is length of playground and y is the breadth of playground.

$\sf\small\underline\blue{Calculation\: for\: first\: equation:-}$

$\tt{\implies Area\:_{(playground)}=length*breadth}$

$\tt{\implies x*y=420}$

$\tt{\implies x=\dfrac{420}{y}------(i)}$

$\sf\small\underline\blue{Calculation\: for\:second\: equation:-}$

$\tt{\implies Length\:_{(increased\:by\:7)}*breadth\:_{(decreased\:by\:5)}=Area\:_{(remain\: same)}}$

$\tt{\implies (x+7)*(y-5)=x*y}$

$\tt{\implies xy-5x+7y-35=xy}$

$\tt{\implies -5x+7y=35-----(ii)}$

In eq (ii) putting the value of x=420/y :-]

$\tt{\implies -5*\dfrac{420}{y}+7y=35}$

$\tt{\implies \dfrac{-2100}{y}+7y=35}$

$\tt{\implies \dfrac{-2100+7y^2}{y}=35}$

$\tt{\implies 7y^2-35y-2100=0}$

Here dividing by 7 on both sides:-]

$\tt{\implies y^2-5y-300=0}$

Now splitting the middle term here:-]

$\tt{\implies y^2-20y+15y-300=0}$

$\tt{\implies y(y-20)+15(y-20)}$

$\tt{\implies (y+15)(y-20)=0}$

$\tt{\implies \therefore\:y=-15\:\:,20}$

Here negative values can't be the dimensions of rectangle so, we take y=20 here:-]

$\tt{\implies breadth\:_{(playground)}=20m}$

Now putting the value of y=20 in eq (i) :-]

$\tt{\implies x=\dfrac{420}{y}}$

$\tt{\implies x=\dfrac{420}{20}}$

$\tt{\implies x=21m}$

$\sf\large{Hence,}$

$\sf{\implies The\: length\:_{(playground)}=21\:m}$

$\sf{\implies The\: breadth\:_{(playground)}=20\:m}$