Question

Look at the triangle ABC. What is the length of the side AB of the triangle? A.) 3 B.) 5 C.) Square root of 6 D.) Square root of 13

Answer 1

sqrt(13) = c

Explanation:

The length of BC = 4-2 =2

The length of AC = 5-2 =3

We can use the Pythagorean theorem

a^2 + b^2 = c^2

2^2 + 3^2 = c^2

4+9 = c^2

13 =c^2

Take the square root of each side

sqrt(13) = c

Answer 2

The answer is option D

Explanation:

To find the length of AB we use the formula

`\sqrt{ ({x _(1) - x_(2)})^(2) + ({y_(1) - y_(2) })^(2) }`

Where

(x1 , y1) and (x2 , y2) are the points

From the question

A is (4 , 5) B is (2 , 2)

So the length of AB is

`|AB| = \sqrt{ ({4 - 2})^(2) + ({5 - 2})^(2) }`

`|AB| = \sqrt{ {2}^(2) + {3}^(2) }`

`|AB| = √(4 + 9)`

We have the final answer as

`|AB| = √(13)`

Hope this helps you