Question

The area of a rectangular field whose length is twice its breadth is 2450 m². Find the perimeter of the
field​

Answer 1

Answer:

Perimeter of the field = 210m.

SOLUTION

Given The Area of the Rectangle = 2450 m².

Let us Assume that the breadth(b) of the rectangular field as 'x' m →(1)

∵It is given that :- length is twice its breadth.

Length(l) of the rectangular field = 2x →(2)

Area of rectangle = Length × Breadth = l×b

Area of the rectangular Field  = x × 2x

Area of the rectangular Field = 2x² → (3)

$\implies$

2x² = 2450

$\implies$

$\sf x^2 = \dfrac{2450}{2}$

$\implies$

x² = 1225

∵ x² = 1225

x =√1225

∴ The Breadth (x) of the rectangular field = 35 m.

Let us substitute x = 35 in (2) then,

Length of the rectangular field (l) = 2 × 35 = 70m.

THE RECTANGULAR FIELD IS:-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 70m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 35m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

PERIMETER

Perimeter = 2 × (Breadth + Length) = 2 (l+b)

Here,

l = 35m.

b = 70m.

Perimeter  = 2 × (35 + 70)

Perimeter = 2 × 105

Perimeter = 210 m.