Question

um ponto é escolhido aleatoriamente dentro do retângulo abaixo. qual é a probabilidade de que o ponto esteja dentro do triângulo? (a figura pode não estar desenhada em escala). show your work here enter your answer check

Explanation:

Step1: Calculate rectangle area

The area of a rectangle is given by $A_{r}=l\times w$. Here, $l = 17$ and $w=13$, so $A_{r}=17\times13 = 221$.

Step2: Calculate triangle area

The area of a right - triangle is given by $A_{t}=\frac{1}{2}\times b\times h$. Here, $b = 11$ and $h = 7$, so $A_{t}=\frac{1}{2}\times11\times7=\frac{77}{2}=38.5$.

Step3: Calculate probability

The probability $P$ that a randomly - chosen point in the rectangle is in the triangle is the ratio of the area of the triangle to the area of the rectangle. So $P=\frac{A_{t}}{A_{r}}=\frac{38.5}{221}=\frac{77}{442}\approx0.174$.

Answer:

$\frac{77}{442}$