The height drawn to the base of the isosceles triangle is 12 cm, and the lateral side is 13 cm.

The height drawn to the base of the isosceles triangle is 12 cm, and the lateral side is 13 cm. Determine the area and perimeter of the rectangle.

1. The tops of the triangle – A, B, C. Side AB = 13 cm. BC = 13 cm. BK = 12 – height. P is the perimeter of the triangle. S is the area of the triangle.

2. We calculate the length of the segment AK, applying the formula of the Pythagorean theorem:

AK = √AB² – BK² = √13² – 12² = √169 – 144 = √25 = 5 cm.

3. AK = CK, since the height in an isosceles triangle serves as the median (divides the AC into two equal segments).

4. AC = AK + CK = 5 + 5 = 10 cm.

5.P = AC + AB + BC = 10 + 13 + 13 = 36 cm.

6. S = AC / 2 x BK = 10/2 x 12 = 60 cm².