Question

In ABC AD=12 , AB=15,and AC=13 what is BC

Answer 1

Given:

A triangle ABC where AD = 12 units, AB = 15 units, and AC = 13 units.

To find:

The length of BC.

Solution:

According to the Pythagorean theorem, the square of the hypotenuse will be equal to the sum of the squares of the other two sides.

There are 2 triangles, ACD and ABD in triangle ABC.

In triangle ACD, AC is the hypotenuse.

In triangle ABD, AB is the hypotenuse.

Assume the length of CD is x and the length of DB is y.

For triangle ACD,
`AC^(2) = AD^(2) + CD^(2) .`

`13^(2) = 12^(2) +x^(2) .`

`x^(2) = 169-144 = 25.`

`x = √(25) = 5.`

For triangle ABD,
`AB^(2) = AD^(2) + BD^(2) .`

`15^(2) = 12^(2) +y^(2) .`

`y^(2) = 225-144 = 81.`

`y = √(81) = 9.`

`CB=CD+DB = 5+9=14` units.

So BC is option C. 14 units long.