Question

Which expression represents the perimeter of a rhombus with diagonal lengths 8a and 10a?

Answer 1

Answer:

4a$\sqrt{x}$41

Step-by-step explanation:

12*2+9x2= Perimeter.

Answer 2

The perimeter P of rhombus is given as

$\rm\bold{ P = 4\sqrt{41}a }$

The diagonals of rhombus bisect each other at right angles and it has same perimeter as that of a square.

From this property stated above we can formulate  side of rhombus is below in equation (1)

Side and  diagonals of rhombus have following relation

$\rm Let \; the \; side \; of\; rhombus = s\\Length\; of \; first \; diagonal = 8a\\ Length\; of \; second \; diagonal = 10a\\\\According \; to \; the \; identity\; for\; area \; of\; rhombus \\ s^2 = (p/2)^2 +(q/2)^2 ....(1) \\where \; p \; and\; q \; are\; the \; diagonals.$

so

$\rm s^2 = (10a/2)^2 + (8a/2)^2\\s^2 = 25a^2 + 16a^2 = 41 a^2 \\s= \sqrt{41}a ......(2)$

Equation (2) represents side of rhombus

So the perimeter P of rhombus is given as

$\rm P = 4\times s$

$\rm\bold{ P = 4\sqrt{41}a }$

The perimeter P of rhombus is given as

$\rm\bold{ P = 4\sqrt{41}a }$

For more information please refer to the link below

https://brainly.com/question/24438053