Question

Can I please have help with question 2) a and b

Answer 1

`(10√(6) )/(3)` and
`(11√(3) )/(3)`

Explanation:

(a)

A =
`(1)/(2)` × 4
`√(2)` ×
`(5)/(√(3) )`

= 2
`√(2)` ×
`(5)/(√(3) )`

=
`(10√(2) )/(√(3) )` ×
`(√(3) )/(√(3) )` ← rationalise the denominator

=
`(10√(6) )/(3)` units²

(b)

Using Pythagoras' identity in the right triangle

let hypotenuse be h , then

h² = (4
`√(2)` )² + (
`(5)/(√(3) )` )²

= 32 +
`(25)/(3)`

=
`(96)/(3)` +
`(25)/(3)`

=
`(121)/(3)` ( take the square root of both sides )

h =
`\sqrt{(121)/(3) }` =
`(11)/(√(3) )` ×
`(√(3) )/(√(3) )` ← rationalise the denominator

h =
`(11√(3) )/(3)`