# FIND SIDE LENGTH OF SQUARE FROM DIAGONAL

Find the length of each side.

Problem 1 :

Solution :

AB = x, BD = 2√2, AD = x

Using Pythagorean theorem.

AB2 + AD2 = BD2

x2 + x2 = (2√2)2

2x2 = 8

Dividing 2 on both sides.

8/2 = 2x2/2

x2 = 4

x = 2

So, the length of each side is 2.

Problem 2 :

AB = x, BD = 40√2, AD = x

Using Pythagorean theorem

(BD)2 = (AB)2 + (AD)2

(40√2)2 = x2+ x2

1600 × 2 = 2x2

3200 = 2x2

Dividing 2 on both sides.

3200/2 = 2x2/2

x2 = 1600

x = 40

So, the length of each side is 40.

Problem 3 :

Solution :

AB = x, BD = 6, AD = x

Using Pythagorean theorem

(BD)2 = (AB)2 + (AD)2

62 = x2+ x2

36 = 2x2

Dividing 2 on both sides.

36/2 = 2x2/2

x2 = 18

x = √(9 × 2)

x = 3√2

So, the length of each side is 3√2.

Problem 4 :

A square has a diagonal with the length of 8√6 meters. What is the length of the sides ?

Solution :

A square has a diagonal with the length of 8√6 meters. Let s be the length of the sides of the square.

Using Pythagorean theorem.

(BD)2 = (AB)2 + (AD)2

(8√6) 2 = s2 + s2

64 × 6 = 2s2

384 = 2s2

Dividing 2 on each sides.

384/2 = 2s2/2

192 = s2

s = √(64 × 3)

s = 8√3

So, the length of each side is 8√3 .

Problem 5 :

A square has a diagonal 12√6. What is the measure of the sides of the square ?

Solution :

A square has a diagonal is 12√6. Let x be the sides of the square.

Using Pythagorean theorem.

(BD)2 = (AB)2 + (AD)2

(12√6)2 = x2 + x2

(12√6)2 = 2x2

144 × 6 = 2x2

864 = 2x2

Dividing 2 on both sides.

864/2 = 2x2/2

432 = x2

x = √432

x = √(16 × 27)

= √(4 × 4 × 9 × 3)

= 4 × 3√3

x = 12√3

So, the measure of the sides of the square is 12√3.

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