Question

if the area of the square is 729m2 then its side and length of diagonal will be

Answer 1

Given:

• Area of square = 729 m²

To find:

• Side of the square
• Length of diagonal of the square

Solution:

We know that,

$\boxed {\mathfrak {\pink {Area\ of\ square = s^{2}}}}$

Substitute the values,

729 = s²

$\sf \sqrt{729} = s$

$\bigstar {\bf {\blue {27\ m = s}}}$

Now,

We know that in a square, all the sides are equal and all the angles are of 90° (or are right-angled)

So, Using Pythagoras Theorem;

H² = P² + B²

Where,

H denotes Hypotenuse

P denotes Perpendicular

B denotes Base

Substitute the values,

H² = 27² + 27²

H² = 729+729

H² = 1458

$\sf H = \sqrt{1458}$

$\bigstar {\bf {\blue {H = 38.18\ m}}}$

☆ You can even use the formula for finding the diagonal of the square:

$\boxed {\mathfrak {\red {d = \sqrt {2 \times area}}}}$

Answers:

• Side of the square is 27 m.
• Diagonal of the square is 38.18 m.