Chapter 12.4, Problem 21E

(a)

To determine

To Explain: How you know that any triangle made out of equilateral triangle is equilateral.

Answer to Problem 21E

All equilateral triangle has equal angles and equal sides.

Explanation of Solution

Given:

  

All equilateral triangle has equal angles and equal sides.

Thus

Assuming the length of side be $x$ then second item in the table is having a length of side $2x$ and it goes on.

(b)

To determine

To Find: The area of first four triangle in the pattern.

Answer to Problem 21E

  $\begin{array}{l}1=1sq.unit\\ 2=4sq.unit\\ 3=9sq.unit\\ 4=16sq.unit\end{array}$

Explanation of Solution

Given:

  

The area of first four triangles are

  $\begin{array}{l}1=1sq.unit\\ 2=4sq.unit\\ 3=9sq.unit\\ 4=16sq.unit\end{array}$

(c)

To determine

To Find: Any pattern in the areas. Predict the area of the seventh triangle in the pattern.

Answer to Problem 21E

  $49sq.units$

Explanation of Solution

Given:

  

The pattern in the area is

Let the number of triangle be $n$

Then

Area be $n^2$

Thus

Area of seventh triangle is

  $n^2=7^2=49sq.units$