Question

7. Perimeter of a rectangular field 50 m long and 30 m
wide is equal to the perimeter of a square field. Find
the area of the square field.​

Answer 1

Answer:

Answer

The area of the square field is 1600m²

\bf\large{\underline{Given}}

Given

The perimeter of a rectangular field is equal to the perimeter of a square field.

The length and breadth of the rectangular field is 50m and 30m

\bf\large{\underline{To Find :}}

ToFind:

The area of the square field

\bf\large{\underline{Formula \: to \: be \: used : }}

Formulatobeused:

★Perimeter of a rectangle = 2(l+b)

★Perimeter of a square = 4l

★ Area of a square = l²

\bf\large{\underline{Solution :}}

Solution:

Let us consider the length of the side of the square field be x m

\underline{\sf\dag \: \: According \: to \: question : }

†Accordingtoquestion:

\sf\implies perimeter \: of \: rectangle = perimeter \: of \: square⟹perimeterofrectangle=perimeterofsquare

\begin{gathered} \sf\implies 2(50+30) = 4x \\\\ \sf\implies 2\times 80 = 4x \\\\ \sf\implies x = \dfrac{\cancel{160}}{\cancel{4}} \\\\ \sf\implies x = 40 \end{gathered}

⟹2(50+30)=4x

⟹2×80=4x

⟹x=

4

160

⟹x=40

Now the area of the square field is :

\begin{gathered}\sf ↦Area \ of \ square= 40^{2} \\\\ \sf ↦ Area \: of \: square= 1600 \end{gathered}

↦Area of square=40

2

↦Areaofsquare=1600

Therefore , the area of the square field is 1600m²