The area of an isosceles triangle is 12. The height drawn to its base is 4. Find the perimeter of this triangle.

Let us denote by a the length of the base of this isosceles triangle.

According to the condition of the problem, the area of ​​this triangle is 12, and the length of the height drawn to its base is 4.

Applying the formula for the area of ​​a triangle in terms of the length of a side and the height drawn to that side, we can compose the following equation:

a * 4/2 = 12

solving which, we get:

a * 2 = 12;

a = 12/2 = 6.

Consider one of the right-angled triangles by which the height drawn to its base divides this isosceles triangle.

In such a right-angled triangle, the hypotenuse is the lateral side of the isosceles triangle, one of the legs is half of the base of the isosceles triangle, and the second leg is the height of the isosceles triangle.

Trying on the Pythagorean theorem, we find the length of the lateral side:

√ (4 ^ 2 + (6/3) ^ 2) = √ (4 ^ 2 + 3 ^ 2) = √ (16 + 9) = √25 = 5.

Find the perimeter of this triangle:

5 + 5 + 6 = 10 + 6 = 16.

Answer: The perimeter of this triangle is 16.