ISO triangle

Calculate the area of an isosceles triangle KLM if its sides' length is in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.

Correct result:

S =  6533.4 mm²

Solution:

$$\begin{gathered} k=l={\displaystyle \frac{4}{4+4+3}}\cdot 377=137.091mm \\ m={\displaystyle \frac{3}{4+4+3}}\cdot 377=102.818mm \\ {h}^2=k^2-(m\mathrm{/}2{)}^2 \\ h=\sqrt{137.091^2-51.409^2}=127.087mm \\ S={\displaystyle \frac{1}{2}}mh={\displaystyle \frac{1}{2}}\cdot 102.818\cdot 127.087=6533.4{\text{mm}}^2 \end{gathered}$$

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