Chapter 9, Problem 4RP

To determine

To find:The perimeter of the rhombus

Answer to Problem 4RP

The perimeter of the rhombus is $P=40$

Explanation of Solution

Given information:The following information has been given

  $AE=6$

  $BE=8$

Formula used:The diagonals of a rhombus are perpendicular

Calculation:We know that the diagonals of a rhombus are perpendicular. Hence, applying Pythagoras theorem to the right triangle AEB, we get

  $A{E}^2+B{E}^2=A{B}^2$

Hence, we get

  $6^2+8^2=A{B}^2\to AB=10$

Now, we know that for a rhombus,

  $P=4AB=4(10)=40$