Find Perimeter of Rhombus from Diagonals | Geometry

How do we find the perimeter of a rhombus from the diagonals? If we're given the diagonals of a rhombus, we can find the perimeter pretty easily using the Pythagorean theorem, we'll see how in today's video geometry lesson!

All we need to do is recall a rhombus is an equilateral parallelogram. Since it is equilateral all of its sides are congruent, so we only need to find one side length then multiply that by four to get the perimeter. Since a rhombus is a parallelogram, its diagonals bisect each other. This allows us to prove that the diagonals also are perpendicular to each other, and so actually cut the rhombus into four congruent right triangles. Now we can simply use the Pythagorean theorem to solve for a side! Then multiply by 4! And that is the perimeter!

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[BubonicBaby_mk]

Watching this during a math test, thanks bro

[jeddunread]

Finally a youtube video on this. Helped me a ton. Thanks!

[cleanheart]

Sir you explained very well I was searching it for hours and then found it it helped me a lot ...Thank you sir

[aashsyed]

Wow! Such a super

Thanks for these joyful moments!!!

[Evxtro]

Thanks, this helped me study for my test😭

[riteshramaswamy]

My exams are very near and i still didnt understand how to find the perimeter of a rhombus with only it diagonals, thank u so much for this very clearly elaborated and simply explained session sir

[aashsyed]

such a solid explanation!
never seen such clever things!
awesome
by the way, what are you using to write on?

[tomkerruish]

You don't have to divide the diagonal lengths by 2, since you wind up multiplying by 4. If d1 and d2 are the lengths, then the perimeter is 2 sqrt(d1² + d2²), i.e. twice the length of the hypotenuse of a right triangle with legs of lengths d1 and d2.

[dracyt]

Sir if the d1 is 15 and d2 is 20 then what is the perimeter please tell me with solution