Question

The area of a square 20cm .calculate the length of a diagonal of the square, correct to two significant figure

Answer 1

Answer :-

• Length diagonal of square = 12.64 cm

Given :-

• Area of square = 20 cm²

To Find :-

• Length diagonal of square = ?

Explanation :-

As we know, we have the area of square and we need find the length of the diagonal of square. In order to find the length of diagonal, first we need to find the side of square.

Let the side of square to be 'x' cm.

$\blue { \boxed { \bigstar \; \text{\bf Area of square = \bf (Side)^2 } \; \bigstar }}$

$\sf : \; \leadsto (Side)^2 = 20 \; \; cm^2$

$\sf : \; \leadsto (x)^2 = 20 \; \; cm^2$

$\sf : \; \leadsto x= \sqrt{20} \; \; cm$

$\green { \sf : \; \leadsto x= 4 \sqrt{20} \; \; cm \qquad \star }$

Now finding the diagonal,

$\blue { \boxed { \bigstar \; \text{\bf Diagonal of square = \bf Side \sqrt{2} } \; \bigstar }}$

$\sf : \; \leadsto Side \; \sqrt{2}$

$\sf : \; \leadsto 4 \; \sqrt{5} \times \sqrt{2}$

$\sf : \; \leadsto 4 \; \sqrt{5 \times 2}$

$\sf : \; \leadsto 4 \; \sqrt{10}$

$\sf : \; \leadsto 4 \times 3.16 \qquad \quad \bf {[\sqrt{10} = 3.16 \; \; \; \; approx.]}$

$\red { \underline { \boxed { \sf : \; \leadsto 12.64 \; \; cm \quad \star }}}$

Hence, the diagonal of the square is 12.64 cm.