# The perimeter of an isosceles triangle is 250 and the lateral side is 85. Find the area of the triangle.

June 29, 2021 | education

| To find the area of a triangle, we will use Heron’s formula. To do this, we need to know all the sides of the triangle. We know the side of the triangle. Since the triangle is isosceles by condition, its two sides (a and b) are equal and their lengths are 85 cm.Let’s find the length of the base (c):

c = P – a – b,

where P is the perimeter, a, b and c are the sides of the triangle.

c = 250 – 85 – 85 = 80 (cm).

Heron’s formula:

S = √ (p (p – a) (p – b) (p – c)),

where S is the area of the triangle; p is the semi-perimeter of the triangle.

p = P / 2 = 250/2 = 125 (cm).

Substitute the values we know:

S = √ (125 * (125 – 85) * (125 – 85) * (125 – 80)) = √ (125 * 40 * 40 * 45) = √9000000 = 3000 (cm square)

Answer: 3000 cm square.

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