Question

2) Qual a área do triângulo ABC.

Answer 1

$\text{Primeiramente vamos determinar o comprimento do lado}\ \overline{BC}:\\\\(\overline{AB})^2=(\overline{AC})^2+(\overline{BC})^2\\\\(\overline{BC})^2=(\overline{AB})^2-(\overline{AC})^2\\\\\overline{BC}=\sqrt{(\overline{AB})^2-(\overline{AC})^2}\\\\\overline{BC}=\sqrt{(85m)^2-(75m)^2}\\\\\overline{BC}=\sqrt{(85m+75m)\cdot(85m-75m)}\\\\\overline{BC}=\sqrt{(160m)\cdot(10m)}\\\\\overline{BC}=\sqrt{1600m^2}\\\\\overline{BC}=40m\\\\\\\text{Por fim, resolvemos o que se pede:}$

$A=\dfrac{\overline{BC}\times\overline{AC}}{2}\\\\\\A=\dfrac{(40m)\cdot(75m)}{2}\\\\\\A=20m\cdot75m\\\\\boxed{A=1500m^2}$

Answer 2

(85m)²=(75m)²+x²=(85m)²-(75m)²=x²

x=10m

Área=(axb)/2=(10*75)/2=375m²