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, $AC^{2} = AD^{2} + CD^{2} .$

$13^{2} = 12^{2} +x^{2} .$

$x^{2} = 169-144 = 25.$

$x = \sqrt{25} = 5.$

For triangle ABD, $AB^{2} = AD^{2} + BD^{2} .$

$15^{2} = 12^{2} +y^{2} .$

$y^{2} = 225-144 = 81.$

$y = \sqrt{81} = 9.$

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

So BC is option C. 14 units long.