Let AD⊥BC be in D, AD=x cm, CD=y cm, and BD= 14-y cm.

Then △ACD, AC? =AD？ +CD？ So 13? =x？ +y？ ( 1)

△ in △ABD，AB？ =AD？ +BD？ So 15? =x？ +( 14-y)？ (2)

The solutions of (1) and (2) give y=5cm and x= 12cm.

So the area of △ABC is ad * BC/2 =12 *14/2 = 84cm?

nature

1. On the plane, the sum of the interior angles of a triangle is equal to 180 (interior angle sum theorem).

2. On the plane, the sum of the outer angles of a triangle is equal to 360 (the theorem of the sum of outer angles).

3. On the plane, the outer angle of a triangle is equal to the sum of two non-adjacent inner angles.

Inference: An outer angle of a triangle is greater than any inner angle that is not adjacent to it.

4. There are at least two acute angles among the three internal angles of a triangle.

5. At least one angle in the triangle is greater than or equal to 60 degrees, and at least one angle is less than or equal to 60 degrees.

6. The sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side.

7. In a right triangle, if an angle is equal to 30 degrees, then the right side opposite to the 30-degree angle is half of the hypotenuse.