Question

Question 8
I always make the same mistake
It’s urgent

Answer 1

`AB=4√(5)` (Which is the same as
`√(80)`)

Explanation:

In order to find the length of AB, we first need to know the length of AC.

The length of the sides for ACD are

`a=2\\b=?\\c=10`

Knowing these values, we can plug them into the pythagorean theorem and solve for the missing side, b

`a^2+b^2=c^2\\\\b^2=c^2-a^2\\\\b=√(c^2-a^2) \\\\b=√((10)^2-(2)^2) \\\\b=√(100-4)\\ \\b=√(96)`

This means that
`AC=√(96)`

Now, let us find the values of a,b and c for our second triangle

`a=4\\b=x\\c=√(96)`

And now time for the pythagorean theorem

`b=√(c^2-a^2) \\\\b=\sqrt{(√(96))^2-(4)^2 } \\\\b=√(96-16)\\\\b=√(80) \\\\b=4√(5)`

This means that
`AB=4√(5)` (Which is the same as
`√(80)`)