Question

bart found 20 quadrilaterals in his classroom. he made a venn diagram using the properties of the quadrilaterals, comparing those with four equal side lengths (e) and those with four right angles (r). given that a randomly chosen quadrilateral has four right angles, what is the probability that the quadrilateral also has four equal side lengths? express your answer in percent form, rounded to the nearest whole percent. 25% 33% 40% 67%

Explanation:

Step1: Identify relevant values

We want to find $P(E|R)$. By the formula of conditional - probability $P(E|R)=\frac{P(E\cap R)}{P(R)}$. From the Venn - diagram, the number of quadrilaterals with four right angles $n(R)=2 + 6=8$, and the number of quadrilaterals with four right angles and four equal side lengths $n(E\cap R)=2$.

Step2: Calculate the probability

The probability $P(E|R)=\frac{n(E\cap R)}{n(R)}$. Substituting the values, we get $P(E|R)=\frac{2}{8}=0.25$.

Step3: Convert to percentage

To convert the decimal to a percentage, we multiply by 100. So $0.25\times100 = 25\%$.

Answer:

25%