Chapter 9.4, Problem 18PSB

To determine

To Calculate: The length of the other diagonal.

Answer to Problem 18PSB

The length of the other diagonal is $\frac{10}{\sqrt{2}}$

Explanation of Solution

Given information:

The perimeter of rhombus is $8\sqrt{5}$ and

one diagonal has a length of $4\sqrt{2}$

Formula used:

Area of rhombus = $\frac{1}{2}\times d_1\times d_2$

Calculation:

Here, $P=4a$ (“ P ” is perimeter and “ a ” is side)

  $8\sqrt{5}=4a$

  $a=2\sqrt{5}$

And, $d_1=4\sqrt{2}$

And, area = $a^2$

  →$2\sqrt{5}\times 2\sqrt{5}=4\times 5=20$

And, area of rhombus = $\frac{1}{2}\times d_1\times d_2$

  $20=\frac{1}{2}\times 4\sqrt{2}\times d_2$

  $d_2=\frac{10}{\sqrt{2}}$

Conclusion: Hence,the length of the other diagonal is $\frac{10}{\sqrt{2}}$