# Isosceles III

The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.

Correct result:

p =  116.3 cm

#### Solution:

$S = \dfrac{ah}{2} \ \\ 416 = \dfrac{ 17 \cdot h}{2} \ \\ h = 48.94 \ cm \ \\ \ \\ b^2 = h^2 + (a/2)^2 \ \\ b = \sqrt{ 48.94^2 + 8.5^2 } = 49.67 \ cm \ \\ \ \\ p = a + 2b = 17 + 2\cdot 49.67 = 116.3 \ \text{cm}$

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