Question

Dados os seguintes vértices de um triangulo (4, −2x); (−7, x) (10,0). Quais devem ser as coordenadas desses vértices para que a área desse triângulo seja 60 u. a. ou seja, qual o valor de ?

Answer 1

$\Large\boxed{\begin{array}{l}\sf Sejam\, A(x_A,y_A),B(x_B,y_B)\,e\,C(x_C,y_C)\\\sf os\,v\acute ertices\,de\,um\,tri\hat angulo.\\\sf A\,\acute area\,deste\,tri\hat angulo\,\acute e\, A=\dfrac{|det\,M|}{2}\\\sf sendo\,M=\begin{bmatrix}\sf x_A&\sf y_A&\sf 1\\\sf x_B&\sf y_B&\sf1\\\sf x_C&\sf y_C&\sf1\end{bmatrix} \end{array}}$

$\Large\boxed{\begin{array}{l}\sf M=\begin{bmatrix}\sf4&\sf-2x&\sf1\\\sf-7&\sf x&\sf1\\\sf 10&\sf0&\sf1\end{bmatrix}\\\sf det\,M=4\cdot(x-0)+2x\cdot(-7-10)+1\cdot(0-10x)\\\sf det\,M=4x-34x-10x\\\sf\\\sf det\,M=-40x\\\sf A=\dfrac{|det\,M|}{2}\\\\\sf 60=\dfrac{|-40x|}{2}\\\\\sf 40x=2\cdot60\\\sf 40x=120\\\sf x=\dfrac{120}{40}\\\\\sf x=3\end{array}}$

Answer 2

Resposta:

oi também preciso saber dessa.