The perimeter of an isosceles triangle is 100, and the lateral side is 29. Find its area.

An isosceles triangle is a triangle in which two sides are equal and are called lateral sides, and the third unequal is based:

AB = BC.

The perimeter of a triangle is the sum of all its sides:

P = AB + BC + AC.

To calculate the length of the base of the speaker you need:

AC = P – (AB + BC);

AC = 100 – (29 + 29) = 100 – 58 = 42 cm.

To calculate the area of ​​a triangle, we will use Heron’s Formula:

S = √p (p – a) (p – b) (p – c); where:

S is the area of ​​the triangle;

p – semi-perimeter (p = P / 2);

a – side AB;

b – aircraft side;

c – speaker side;

p = 100/2 = 50;

S = √ (50 ∙ (50 – 29) ∙ (50 – 29) ∙ (50 – 42)) = √ (50 21 21 8) = √176400 = 420 cm2.

Answer: the area of ​​the triangle is 420 cm2.