Question

the area of a square field is 841 metre square a rectangular field whose length is twice its breadth as its perimeter is equal to the perimeter of the square field find the area of the required rectangular field​

Answer 1

Given:-

• Area of square field is 841 m².
• Perimeter of rectangular field is equal to Perimeter of square field.

To find:-

• Area of rectangular field.

Solution:-

• First we have to find Perimeter of square field for perimeter of rectangular field beacuse Perimeters are equal. So,

⠀⠀⠀

Area of square = side × side

So,

$\implies \sf \: Side \: \times Side = 841 \\ \implies \sf \: {(Side)}^{2} = 841 \\ \implies \sf \: Side \: = \sqrt{841} \\ \implies \sf \: Side \: = 29$

⠀⠀⠀

Side of square field is 29 cm.

⠀⠀⠀

Perimeter of square = 4 × side

Side is 29 cm

So,

$\implies \sf \: 4 \times 29 \\ \implies \sf \: 116$

⠀⠀⠀

Perimeter of square field is 116 cm.

______________________________

Let the Breadth of rectangular field be 'x'.

And length of rectangular field be '2x'.

⠀⠀⠀

Perimeter of rectangular field = Perimeter of square field.

So,

⠀⠀⠀

$\implies \sf \: 2 \times (2x + x) = 116 \\ \implies \sf \: 4x + 2x = 116 \\ \implies \sf \: 6x = 116 \\ \implies \sf \: x = \frac{116}{6} \\ \implies \sf \: x = 19 .33$

⠀⠀⠀

Length of rectangular field is 19.33 m

Breadth of rectangular field is 38.66 m (Beacuse 2 × 19.33 = 38.66)

⠀⠀⠀

Area of rectangle = Length × Breadth

So,

$\implies \sf \: 19.33 \times 38.66 \\ \implies \sf \: 747.2978$

⠀⠀⠀

Therefore,

Area of rectangular field is 747.2978 m²