Chapter 11.7, Problem 16PSB

To determine

To calculate:The ratio of area of equilateral triangleABCand area of equilateral triangle PQR.

Answer to Problem 16PSB

Theratiois $9:16$ .

Explanation of Solution

Given information:

ABC and PQR are equilateral triangles.

AB = 6,

PQ = 8.

Formula used:

Area of equilateral triangle: $A=\frac{s^2}{4}\sqrt{3}$

s = side of equilateral triangle.

Area of triangle is proportional to square of its side.

Calculation:

  

Area of triangle is proportional to square of its side.

The area ratio is as follows:

  $\begin{array}{l}\frac{A(ABC)}{A(PQR)}=\frac{{(AB)}^2}{{(PQ)}^2}\\ \frac{A(ABC)}{A(PQR)}={\left(\frac{AB}{PQ}\right)}^2\\ \frac{A(ABC)}{A(PQR)}={\left(\frac{6}{8}\right)}^2\\ \frac{A(ABC)}{A(PQR)}=\frac{36}{64}\\ \frac{A(ABC)}{A(PQR)}=\frac{9}{16}\end{array}$