Chapter 9.7, Problem 3PSA

a

To determine

To calculate: The value of “ a ” in given equilateral triangle whose base is 4.

Answer to Problem 3PSA

The variable in equilateral triangle (a) = $2\sqrt{3}$

Explanation of Solution

Given information Equilateral triangle with side 4

  $\begin{array}{l}{\text{a}}^2\\ =4^2-2^2\\ =2^2\left(4-1\right)\\ \therefore \text{a}=2\sqrt{3}\end{array}$

b

To determine

To calculate: The value of “ b ” in given equilateral triangle whose altitude is 21.

Answer to Problem 3PSA

The variable in equilateral triangle ( b ) = $14\sqrt{3}$

Explanation of Solution

Given information Equilateral triangle with hypo 21

  $\begin{array}{l}{b}^2={21}^2+{\left(\frac{b}{2}\right)}^2\\ \Rightarrow b^2-{\left(\frac{b}{2}\right)}^2=441\\ \Rightarrow \frac{3}{4}{b}^2=441\\ \Rightarrow b^2=441\times \frac{4}{3}=147\times 4=7\times 7\times 3\times 4\\ \Rightarrow b=7\times 2\times \sqrt{3}=14\sqrt{3}\end{array}$

c

To determine

To calculate: The value of “ x ” in given equilateral triangle whose base is 26.

Answer to Problem 3PSA

The variable in equilateral triangle ( x ) is $13\sqrt{3}$ .

Explanation of Solution

Given information Equilateral triangle with side 26

  $\begin{array}{l}{x}^2={26}^2-{13}^2=39\times 13\\ \Rightarrow x=13\sqrt{3}\end{array}$