Chapter 11, Problem 20CT

(a)

To determine

To Find: The probability that the point is inside $\Delta ABD$ .

Answer to Problem 20CT

  $\frac{1}{2}$

Explanation of Solution

Given: A point is chosen randomly in $\Delta ABC$.

  

Since we need to find the probability that the point is inside $\Delta ABD$ .

  $\Delta ABDand\Delta ABC$ both trinagles have the common base.

Therefore

When two similar triangles have the same base then their areas are the ratio of their heights.

Thus

  $ratio=\frac{6}{12}=\frac{1}{2}$

Hence, the probability is $\frac{1}{2}$ .

(b)

To determine

To Find: The probability that the point is inside $\Delta BDE$ .

Answer to Problem 20CT

  $\frac{3}{14}$

Explanation of Solution

Given: A point is chosen randomly in $\Delta ABC$.

  

Since we need to find the probability that the point is inside $\Delta BDE$ .

  $\Delta ABDand\Delta ABC$ both trinagles have the common base $BD$ .

Therefore

When two similar triangles have the same base then their areas are the ratio of their heights.

Thus

  $ratio=\frac{3}{3+4}=\frac{3}{7}\times \frac{1}{2}=\frac{3}{14}$

Hence, the probability is $\frac{3}{14}$ .