Question

What is the exact perimeter of kite UVWX?

Answer 1

Answer : The exact perimeter of kite UVWX is, 28 unit.

Step-by-step explanation :

First we have to determine the length UV by using pythagoras theorem.

`(UV)^2=(OU)^2+(OV)^2`

Given:

OU = 3 unit

OV = 4 unit

`(UV)^2=(OU)^2+(OV)^2`

`(UV)^2=(3)^2+(4)^2`

`(UV)^2=9+16`

`(UV)^2=25`

`UV=√(25)`

`UV=5`

Now we have to determine the length UX by using pythagoras theorem.

`(UX)^2=(OU)^2+(OX)^2`

Given:

OU = 3 unit

OX = 9 unit

`(UX)^2=(OU)^2+(OX)^2`

`(UX)^2=(3)^2+(9)^2`

`(UX)^2=9+81`

`(UX)^2=90`

`UX=√(90)`

`UX=9.5`

Now we have to determine the perimeter of kite UVWX.

Perimeter of kite UVWX = Sum of 4 sides

Perimeter of kite UVWX = Length UV + Length VW + Length XW + Length UX

As per image,

UV = VW = 5 unit

and,

UX = XW = 9.5 unit

Thus,

Perimeter of kite UVWX = 5 + 5 + 9.5 + 9.5

Perimeter of kite UVWX = 28 unit

Therefore, the exact perimeter of kite UVWX is, 28 unit.