ISO Triangle V2

The perimeter of RR triangle (isosceles) is 474 m, and the base is 48 m longer than the arms. Calculate the area of this triangle.

Correct answer:

S =  10026.4 m²

Step-by-step explanation:

$$\begin{gathered} 474=2a+b \\ b=a+48 \\ 474=3a+48 \\ a=142 \\ b=a+48=190 \\ {h}^2=a^2-(b\mathrm{/}2{)}^2 \\ h=\sqrt{142^2-(190\mathrm{/}2{)}^2} \\ h=105.541 \\ S={\displaystyle \frac{bh}{2}}={\displaystyle \frac{190\cdot 105.541}{2}} \\ S=10026.4{\text{m}}^2 \end{gathered}$$

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