Question

The diagonal of a square is 7 cm find the length of the side of the square

Answer 1

by pythagoras theorem
side² + side² = diagonal²
a² + a² = 7².........[let side be "a"]
2a² = 49
a² = 49/2
a = √ (49/2)
a = √49/√2
a = 7/√2
a = (7/√2)(√2/√2)
a = 7√2/2
side = 7√2/2 cm

Answer 2

Question

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

Given:-

$\large \purple \leadsto$Length of diagonals = 7 cm

To Find:-

$\large \purple \leadsto$Length of each side of square.

Solution

Diagram is in attachment.

Let's solve,

$\large \purple \leadsto$ABCD is a square.

$\large \purple \leadsto$AB = CD = AD = BC

$\large \purple \leadsto$AC is one of diagonals of square ABCD.

$\large \purple \leadsto$Angle ADC = 90°

$\large \purple \leadsto$Now,∆ADC is right angled ttiangle.

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.

Using pythagoras theorem :-

$\large\pink\leadsto$x² + x² = 7²

$\large\pink\leadsto$2x² = 49

$\large\pink\leadsto$x = √$\sf{\frac{49}{2} }$

$\large\pink\leadsto$x = 7√$\sf{ \frac{1}{2} \: cm}$

Required Answer

$\sf{ \sqrt[7]{ \frac{1}{2} \: cm}}$