Question

The side of a square measures 6 cm. What is the exact length of the diagonal of the square

Answer 1

The Sides of square are equal.

sideA, B, C, D = 4cm

Explanation:

In triangle ABC,

By Pythapgoras Theorem,

AC square= AB square + BC Square

AC square =4 square + 4 square

AC square = 16 + 16

AC = √32

AC = √16x2

AC = 4√2

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Answer 2

6
`√(2)` cm

Explanation:

the diagonal divides the square into 2 right angles with legs 6 cm and hypotenuse h is the diagonal.

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares of the other 2 sides.

h² = 6² + 6² = 36 + 36 = 72 ( take square root of both sides )

h =
`√(72)` =
`√(36(2))` =
`√(36)` ×
`√(2)` = 6
`√(2)`

the diagonal is 6
`√(2)` cm