Chapter 11.7, Problem 19WE

(a)

To determine

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

Answer to Problem 19WE

  $\frac{3}{4}$

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

  $\frac{b_1}{b_2}=\frac{6}{8}=\frac{3}{4}$

Hence, $\frac{3}{4}$

(b)

To determine

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

Answer to Problem 19WE

  $\frac{3}{7}$

Explanation of Solution

Given:

  

In triangles $IandIII$

  $\begin{array}{l}ar(I)+ar(II)=ar(III)\\ 1+\frac{ar(II)}{ar(I)}=\frac{ar(III)}{ar(I)}\\ 1+\frac{4}{3}=\frac{ar(III)}{ar(I)}\\ \frac{ar(III)}{ar(I)}=\frac{7}{3}\\ \frac{ar(I)}{ar(III)}=\frac{3}{7}\end{array}$

Hence, $\frac{3}{7}$ .