Calculate the Perimeter of the given shape | Side lengths are given as 9, 12, and 15

Learn how to calculate the Perimeter of the given shape. Simple and step-by-step explanation!

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Calculate the Perimeter of the given shape | Side lengths are given as 9, 12, and 15

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Olympiad Mathematics
pre math
Po Shen Loh
Calculate the Perimeter of the given shape

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[juliapigworthy]

My maths skills have atrophied somewhat decades after school so I actually enjoyed rediscovering how to calculate an amount like this using algebra.. thank you for the refresher.

[spiderjump]

Vertical lengths =15+15=30
Horizontal lengths =9+12 +9+12=42
Hence perimeter = 72

[Sam_on_YouTube]

I'm good with visualization. Got it in my head pretty quick. I didn't use a variable. I simply moved the 12 length next to 9 and the overlap is the same as the extra little length. So it forms a 21×15 rectangle. But that's harder to see in your head.

[mikekelly]

Did it in my head in under 10 seconds, but then again I regularly set out foundations, so this thind of stuff is second nature. find it hilarious when kids say"we'll never use that" in maths classes, mathematics is part of life.

[af_]

bro when did i become bad at maths again i was good when i was 18 but after 23 this geometry stuff doesn't come to me instantly. thanks comp sci degree

thanks for the video

[m.r.rodriguez]

I'll use a ruler and solve it way quicker 😎.

[bendaniels]

Your answer is wrong or the shape in the picture should actually be a rectangle. 9 + 12 cannot equal the total of the top or bottom because 9 and 12 overlap. Your answer says that the top and bottom add up to 42. That would mean that the top is 21 which is 9 +12. This cannot be the right answer.

[SusanKas-vsxx]

i agree but that makes the drawing out of scale

[AnonimityAssured]

With a little mental manipulation...

(spoiler alert)

... we could imagine the shape being reduced to one with no internal area, or enlarging to become a rectangle with maximal area. Either way, the perimeter would be twice the sum of the line-lengths shown.

[michaeltelemachus]

You don't actually need to use algebra to work this out; just a (very small) bit of intelligence or perhaps common sense.

[Budrudesill]

If this isn't drawn to scale, it just a trick, not an honest test.

[BaikalTii]

how about calc'ing the actual lengths of the missing sides? the overall perimeter value does not have much use.

[junkerzn]

Another way of visualizing it is to change the shape equivalently. Take the vertical segment middle right and move it leftward until it hits the vertical (15) segment on the left. This also pulls the vertical segment on the lower right leftward. By definition, the additional perimeter gained in the middle from the extension of the horizontal segments is lost on from the two horizontal segments on lower right, so the shape is equivalent.

Now you have a very simple shape:

9
| | A
| |
9 ----+
|
| B
||
12
| | C
| |
12

Where the left vertical is 15. A + B + C must also equal 15. So you have 15 + 15 + 9 + 9 + 12 + 12 = 72.

-Matt

[robinmorritt]

Slide the "12" line to the right so the "horizontal perimeter lines" are 9, 12, (9 + 12). Add the vertical perimeter 15 + 15.
Perimeter of shape = 9 + 12 + 9 + 12 + 15 + 15 = 72

[sandydl]

But that would mean that 9 - x = 0. The diagram would look like a 15 * 9 rectangle with a 12 inch bump out at the bottom right. I would assume that the diagram requires that 0 < 9-x < 9

[GaryBricaultLive]

Something is wrong with this explanation. You cannot simply factor out X and call it good. Doing so means that no matter what value might be assigned to X, the value of the perimeter will be a constant of 72. X must be a value greater than zero otherwise the middle vertical segment will overlap the left vertical segment resulting in the shape that is no longer the original object.
Also, by factoring out X, one cannot work backwards to solve for X given a value for the perimeter as it will no longer be present in the equation.

[BeasoreBilly]

I just made it into a rectangle. I moved the 12 unit segment to the top creating a 21 unit side. Then moved the smallest horizontal segment to the bottom creating another 21 unit side. Then moved all the small vertical segments to the right, creating a 15 unit side. Then added it up to 72.

[silksongreactions]

I just did 15 plus 15 then figured the two horizontal unmarked lines must add up to 9+12

So
15+15+9+9+12+12=72

[ElCidPhysics]

The small horizontal section = y, the larger bottom section = X. Then 9+12-X = Y. So 9+12 = X+Y. So you have 15+15+2(9+12)

[Waldlaeufer]

Perimeter vertical = 2 * 15 = 30
Perimeter horizontal = 2 * (12 + 9) = 42
Perimeter total = 30 + 42 = 72