Question

The diagonal of a square is 7 cm. Find the length of the side of the square .

Answer 1

Given :

• length of diagonal of square = 7 cm

To find :

• Length of each side of square

Solution :

Explanation of diagram ( refer attached picture for diagram ) :-

• ABCD is a square
• AB = CD = Ad = BC ( because length of each side of square is equal )
• AC is one of the diagonals of square ABCD
• Angle ADC = 90° ( because in square adjacent sides are at 90° to each other)
• Now , ∆ADC is a right angled triangle .

Let each side of square be x.

This means that AD= DC = x

∆ADC is a right angled triangle where AD and Dc are at 90° to each other and AC is diagonal.

Now , using Pythagoras theorem :-

=> x²+x² = 7²

=> 2x² = 49

=> x² = 49/2

=> x = √(49/2)

=> x = 7√(1/2) cm

Answer :

$\tt \: Length \: of \: each \: side \: of \: square \: = 7 \sqrt{ \dfrac{1}{2} } \: cm$

Answer 2

$\large\bf \red{\underline{Given:-}}$

• The diagonal of a square is 7 cm.

$\large\bf \red{\underline{To \: Find :-} }$

• The length of the side of the square.

$\large\bf \red{\underline{Solution :- } }$

We know that,

The diagonal of a square is = √2a cm

Hence,

$\sqrt{2} a = 7$

$⇒a = \frac{7}{ \sqrt{2} }$

$⇒a = 4.95$

Hence, the length of the side of the square is 4.95 cm.