The lateral side of an isosceles triangle is 13 cm, and its median, drawn to the base, is 5 cm.

The lateral side of an isosceles triangle is 13 cm, and its median, drawn to the base, is 5 cm. Find the area and perimeter of the triangle.

We know that the median, lowered to the base of an isosceles triangle, divides the base by sex and forms an angle of 90 ° with it. This means that the median divides this triangle into 2 equal right-angled triangles, in which the hypotenuses are the sides, and the legs are the median and half the base.

Hence, by the Pythagorean theorem, we can find half the base:

13² – 5² = 169 – 25 = 144 = 12².

Half base is 12, then:

12 * 2 = 24 cm – the base of the triangle:

P = 13 + 13 + 24 = 50 cm;

S = 1/2 HV * AC = 1/2 * 24 * 13 = 156 cm².