Question

If the area of a square field is 154 sq. cm. find its diameter

Answer 1

The diagonal of a square field (d) = $2\sqrt{77}$ cm

Step-by-step explanation:

Given,

The area of a square field = 154 $cm^{2}$

To find, the diagonal of a square field (d) = ?

Let the area of a square field = a

We know that,

The area of a square field = $a^{2}$

and

The diagonal of a square field (d) = $\sqrt{2}a$

∴ The side of a square field (a) = $\dfrac{d}{\sqrt{2}}$

The area of a square field = $(\dfrac{d}{\sqrt{2}})^2$

⇒$(\dfrac{d}{\sqrt{2}})^2$ = 154

⇒ $\dfrac{d^2}{2}$ = 154

⇒ $d^2$ = 154 × 2 = 308

⇒ d = $\sqrt{308}$

⇒ d = $\sqrt{2\times 2 \times 77}$

⇒ d = $2\sqrt{77}$ cm

∴  The diagonal of a square field (d) = $2\sqrt{77}$ cm

Answer 2

Therefore the diameter of the circle inscribed in the square= the length of each side of the square =$\sqrt{154}$ cm

If the square circumscribed by a circle , then the diameter of the circle is= the length of the diagonal of the square = $2\sqrt{77}$ cm.

Step-by-step explanation:

Given ,the area of a square is 154 square cm.

The length of side of the square=$\sqrt{154}$ cm

Therefore the diagonal of the square is= $l\sqrt{2}$

                                                                 =$\sqrt{154} \sqrt{2}$ cm

                                                                  = $2\sqrt{77}$  cm

Therefore the diameter of the circle inscribed in the square= the length of each side of the square =$\sqrt{154}$ cm

If the square circumscribed by a circle , then the diameter of the circle is= the length of the diagonal of the square = $2\sqrt{77}$ cm.