Chapter 1.1, Problem 11PSB

a.

To determine

To Evaluate: The length of the side HJ of given triangle.

Answer to Problem 11PSB

  $\text{Perimeter of a triangle }\Delta HJK=\frac{75}{2}\text{units}$

Explanation of Solution

Given:

  $\text{In}\Delta HJK,l\left(\overline{HJ}\right)=2\times l\left(\overline{JK}\right)\text{and}l\left(\overline{HJ}\right)=l\left(\overline{HK}\right)$

and $l\left(\overline{HJ}\right)=15$

Concept Used:

Perimeter of a triangle = Sum of length of sides of triangle

Calculation:

As per the given problem

  $l\left(\overline{HJ}\right)=15\Rightarrow l\left(\overline{JK}\right)=\frac{15}{2}\text{ and }l\left(\overline{HK}\right)=15$

Thus, $\text{Perimeter of a triangle }\Delta HJK=\overline{HJ}+\overline{JK}+\overline{HK}=15+\frac{15}{2}+15=\frac{75}{2}\text{units}$

Conclusion:

  $\text{Perimeter of a triangle }\Delta HJK=\frac{75}{2}\text{units}$

b.

To determine

To Evaluate: The length of the side HJ of given triangle.

Answer to Problem 11PSB

  $\text{Length of side HJ of triangle }\Delta HJK=9\text{units}$

Explanation of Solution

Given:

  $\text{In}\Delta HJK,l\left(\overline{HJ}\right)=4x,l\left(\overline{HK}\right)\text{=3}x\text{and}l\left(\overline{JK}\right)=2x$

Perimeter of a triangle = Sum of length of sides of triangle = 63

Concept Used:

Perimeter of a triangle = Sum of length of sides of triangle

Calculation:

As per the given problem

  $\text{In}\Delta HJK,l\left(\overline{HJ}\right)=4x,l\left(\overline{HK}\right)\text{=3}x\text{and}l\left(\overline{JK}\right)=2x$ and

Perimeter of a triangle = Sum of length of sides of triangle = 63 units

  $\begin{array}{l}\text{Thus, Perimeter of a triangle }\Delta HJK=63\text{units}\\ \Rightarrow 4x+3x+2x=63\text{units}\\ \Rightarrow 7x=63\text{units}\\ \Rightarrow x=\frac{63}{7}\text{units = 9 units}\\ \Rightarrow l\left(HJ\right)=4x=4\times \text{ 9 units = 36 units}\end{array}$

Conclusion:

  $\text{Length of side HJ of triangle }\Delta HJK=9\text{units}$