Chapter 11.7, Problem 13CE

(a)

To determine

To Find: Are the region $IandII$ are similar?

Answer to Problem 13CE

No

Explanation of Solution

Given:

  

No.

The region $IandII$ is not similar.

(b)

To determine

To Find: The name of two similar triangles.

Answer to Problem 13CE

  $\Delta ADE\sim \Delta ABC$

Explanation of Solution

Given:

  

Since $DE\parallel BC$

Thus

  $\Delta ADE\sim \Delta ABC$

(c)

To determine

To Find: The ratio of their areas.

Answer to Problem 13CE

  $4:25$

Explanation of Solution

Given:

  

Since $DE\parallel BC$

Thus

  $\Delta ADE\sim \Delta ABC$

Scalar factor of both the triangle is $2:5$

Therefore

Ratio of area

  $2^2:5^2=4:25$

(d)

To determine

To Find: The ratio of region $IandII$ .

Answer to Problem 13CE

  $21:25$

Explanation of Solution

Given:

  

Scalar factor of both the triangle is $2:5$

Therefore

Ratio of area

  $2^2:5^2=4:25$

  $\begin{array}{l}\frac{ar(I)}{ar(II)}=1-\frac{4}{25}\\ \frac{ar(I)}{ar(II)}=\frac{25-4}{25}=\\ \frac{ar(I)}{ar(II)}=\frac{21}{25}\end{array}$