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# The area of a square field is $\frac{1}{4}$ hectare. Find the length of its diagonal in metres.

**Given:**

Area of square = $\frac{1}{4}$ hectare.

**To do:**

We have to find the length of its diagonal in metres.

**Solution:**

We know that,

1 hectare = 10000 sq m

$\frac{1}{4}$ hectare = $\frac{10000}{4}$ sq.m. = 2500 sq.m.

Area of square = 2500 sq.m.

Area of a square = side $\times$ side

2500 = side $\times$ side

2500 = side^{2}

Side=√2500

Side = 50 m

Length of the side of the square field = 50 m.

Diagonal of square = $\sqrt{50^{2} +50^{2}} =50\sqrt{2}$ m.

**The length of the diagonal of the square field is $50\sqrt{2}$ m.**

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