Question

Find the diagonal of a square whose sides are of the given measure.

Given =

Answer 1

The correct answer is 7 times the square root of 6.

Answer 2

7
`√(42)`

Explanation:

The diagonal is the hypotenuse of the right triangle with legs 7
`√(3)`

Use Pythagoras' identity to solve for the diagonal d

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

d² = (7
`√(3)`)² + (7
`√(3)`)²

= 147 + 147

= 294 ( take the square root of both sides )

d =
`√(294)` = 7
`√(42)` ≈ 45.37 ( to 2 dec. places )