Find the area of an isosceles triangle ABC with a lateral side AB = 34 cm and a perimeter of 100 cm.

Let’s denote the triangle ABC
1) Consider ABC – isosceles, AB = BC = 34cm, P = 100cm.
Let’s draw the height of the HV. Because ABC is isosceles, then VN is also the median.
2) AC = 100 – AB – BC
AC = 100 – 34 – 34
AC = 32
since VN – median, then AC = HC = 32: 2 = 16cm
3) Consider a triangle ABN: rectangular, AB = 34 cm, AH = 16 cm.
By the Pythagorean theorem AB2 = AH2 + BH2
BH2 = AB2-AH2
BH2 = 34 * 34 – 16 * 16
BH2 = 1156 – 256
BH2 = 900
HH = 30 cm
4) Because ABC is a triangle, then S = 1/2 * AC * VN
S = ½ * 32 * 30
S = 480cm2
Answer: 480cm2