Question

The area of a square field is 841m.A rectangular field whose length is twice it's breath has its perimeter equal to square field.Find the area of square field

Answer 1

Answer with explanation:

Given: The area of a square field is 841 sq.m

Since side of square = √Area

So, side of square field = $\sqrt{841} =29$

Thus , side of square field = 29 m

Perimeter of square = 4( side) = 4(29) = 116 m

Let x be the breadth of rectangle then 2x be the length

Perimeter of rectangle = 2 (length+breadth) = 2(2x+x)= 2(3x)=6x

As per question, perimeter of rectangle=  Perimeter of square

$\Rightarrow\ 6x=116\\\\\Rightarrow\ x=\dfrac{116}{6}=\dfrac{58}{3}\ m$

Length : $2x =2\dfrac{58}{3}=\dfrac{116}{3}\ m$

Area of rectangle =  length x breadth

$=\dfrac{116}{3}\times\dfrac{58}{3}=\dfrac{6728}{9}\\\\=747\dfrac{5}{9}\ m^2$

Area of rectangle = $747\dfrac{5}{9}\ m^2$