Chapter 11.7, Problem 18WE

(a)

To determine

To Find: The ratio of area of $IandII$ .

Answer to Problem 18WE

  $\frac{1}{2}$

Explanation of Solution

Given:

  

In triangles $IandII$

Height of both triangles are same.

Therefore

If two triangles have equal heights, then the ratio of their areas equal to the ratio of their bases.

Thus

  $\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}$

Hence, $\frac{1}{2}$

(b)

To determine

To Find: The ratio of area of $IandIII$ .

Answer to Problem 18WE

  $\frac{1}{4}$

Explanation of Solution

Given:

  

In triangles $IandIII$

If two triangles are similar.

Thus

  $\frac{b_1}{b_3}=\frac{3}{6}=\frac{1}{2}$

Now

  $\frac{ar(I)}{ar(III)}=\frac{\frac{1}{2}{b}_1{h}_1}{\frac{1}{2}{b}_3{h}_3}=\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}$

Hence,

  $\frac{1}{4}$ .