The area of an isosceles triangle ABC is 48 and the base of AC is 16. Find the perimeter of triangle ABC.

Draw the height BD from the vertex B of the triangle ABC to the base of the AC.

The area of ​​a triangle is half the product of a side by the height drawn to that side. Means:

SABC = 0.5 * AC * BD;

BD = 2 * SABC / AC = 2 * 48/16 = 6.

In an isosceles triangle, the height drawn to the base is the median, hence AD ​​= CD = AC / 2 = 16/2 = 8.

Triangle ABD is rectangular with hypotenuse AB. By the Pythagorean theorem:

AB ^ 2 = AD ^ 2 + BD ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100;

AB = √100 = 10.

Because triangle ABC – isosceles with base AC, then AB = BC = 10.

Knowing all sides of the triangle, we can find its perimeter:

PABC = AB + BC + AC = 10 + 10 + 16 = 36.