Chapter 1.1, Problem 14PSC

a.

To determine

To Find: The percentage of the triangles in the given diagram having $\overline{CT}$ as its side.

Answer to Problem 14PSC

  $37.5\%$

Explanation of Solution

Given:

  

Concept Used:

When the diagonals of rectangle is drawn, we get triangle each of equal area.

Calculation:

Now using the side $\overline{CT}$ , we get three triangles $\Delta CTE,\Delta CTA,\Delta CTX$ . Here we have eight triangles in the given figure.

Thus, the percentage of triangles using the side $\overline{CT}=\frac{3}{8}\times 100=37.5\%$

Conclusion:

Percentage of triangles using the side $\overline{CT}=37.5\%$

b.

To determine

To Find: The percentage of the triangles in the given diagram having $\overline{AC}$ as its side.

Answer to Problem 14PSC

  $25\%$

Explanation of Solution

Given:

  

Concept Used:

When the diagonals of rectangle is drawn, we get triangle each of equal area.

Calculation:

Now using the side $\overline{AC}$ , we get two triangles $\Delta ACT,\Delta ACX$ . Here we have eight triangles in the given figure.

Thus, the percentage of triangles using the side $\overline{AC}=\frac{2}{8}\times 100=25\%$

Conclusion:

Percentage of triangles using the side $\overline{AC}=25\%$