# Math Help

#### China Cat Sunflower

##### Nimrod
Hey, I need some math help. If I had a primitive CAD program I could do this: I'm ordering a spa cover for my inground Jaccuzzi. I'm ordering online, and I have to provide measurements.

The tub is a square with the four corners truncated, or nipped off at 45 deg. It's octagon-ish, but not a true octagon because it doesn't have sides of equal length. The dimension of the square is 84", and the diagonal dimensions, where the four corners are truncated, is 98". So, imagine that you have an 84" square. And you superimpose another 98" square rotated 45 deg. so it nips off the four corners of the first square.

Question: What is the length of the four small sides.

Chris

Hey, I need some math help. If I had a primitive CAD program I could do this: I'm ordering a spa cover for my inground Jaccuzzi. I'm ordering online, and I have to provide measurements.

The tub is a square with the four corners truncated, or nipped off at 45 deg. It's octagon-ish, but not a true octagon because it doesn't have sides of equal length. The dimension of the square is 84", and the diagonal dimensions, where the four corners are truncated, is 98". So, imagine that you have an 84" square. And you superimpose another 98" square rotated 45 deg. so it nips off the four corners of the first square.

Question: What is the length of the four small sides.

Chris

Impossible to determine since the "sides" are not of equal length. and, you haven't told us what kind of cover your intend to put on this tub either...

2(84²)=14112
(√14112)-98=
20.793939239339984099341852833615 inches
(I didn't write out all the logical steps, just the shortest math calculations involved)

2(84²)=14112
(√14112)-98=
20.793939239339984099341852833615 inches
(I didn't write out all the logical steps, just the shortest math calculations involved)

Which leaves 54.6" for the longer sides.

Logic steps:
Figure the diagonal of the 84" square (118.79")
Subtract the large square
Remainder is the height of the two triangles cut off the corners. Since they're 90 degree right triangles, the hypotenuse (remaining side) is twice that

Which leaves 54.6" for the longer sides.

Logic steps:
Figure the diagonal of the 84" square (118.79")
Subtract the large square
Remainder is the height of the two triangles cut off the corners. Since they're 90 degree right triangles, the hypotenuse (remaining side) is twice that

Well when I calculate the hypotapus by the dipthon it is transparent to me the darn thing aint big enough for all of us to get in.

So I figure it'll have to be in shifts, we'll each line up in order of religion first and then alternate denominations, we'll throw some Christians in with some of the Eastern Religions to balance them out, and a couple Bahai in the Judaic line because to balance that end.

Each gets fifteen minutes in the tub and one exists every five minutes so we get a continual flow of conversation. After your initial line you may join the shortest line or the one you are most likely to post.

Conversations may continue while waiting in line, but please remember to shower prior to entering the tub.

Chris will provide purified drinking water only, bring your own covered dish for the event....

Pythagoras is spinning in his tomb as I write this,

flow...

posts 3 and 4 provide the answer...

a scant 20.8 inches

O.K., 20 and about 13/16. Cool beans! Thanks!

Chris

OK Chris...now for the BIG question...do you plan to eat cheese curds and drink longnecks whilst relaxing in your 84x98 " slice of warm circulating liquid heaven? I've been known to put entire Rolling Rock longnecks in my ample maw whilst I imbibe.

All I can find are some scrawny herring and repulsive-tasting anchovies down here. Besides the bones always get stuck in my teeth.

I demand daily reports when it's finished and usable.

flow....

OK Chris...now for the BIG question...do you plan to eat cheese curds and drink longnecks whilst relaxing in your 84x98 " slice of warm circulating liquid heaven?

All I can find are some scrawny herring and repulsive-tasting anchovies down here. Besides the bones always get stuck in my teeth.

I want daily reports when it's finished and usable.

flow....

LOL!

The Jacuzzi was here when we bought the house three years ago. It's now the glorious cool season here in the desert, and I want to drain the tub, clean and polish it, and put new water in for the winter. I replaced the heater last year, but I wanted to get another year out of the topper. Now it's really shot; eaten up by the sun, and I've got to replace it. You might wonder why I didn't just measure the short sides. I'm ordering the top an inch over size because these spa tops tend to shrink a little after some time in the sun. I couldn't just add an inch to every dimension because, obviously, that wouldn't be proportionate with different length sides.

And yes, I intend to relax in the hot tub after my sacred Sunday golf rounds and suck down coldies. Last year we brought a T.V. out and watched the superbowl from the hot tub. How's that for decadence?!

Chris

Cackle, cackle, cackle...delicious sounding diversions...except for the zero weather, I'm happy for you.

flow....

View attachment 306

I'm trying to figure out the X dimension.

Chris

Um, at the risk of being stupid, how long are the base and rise of the triangle for one corner is?

You know, the base dimension and the rise dimension?, for your right triangle in the corner? That is an easy enough set of dimensions...

Then you take that square in inches, and remove that times four from the length and width of your square/rectangle of a spa.

But then, you already knew that Chris...Easiest things first...

v/r

Joshua

I think you just forgot.

Last edited:
Um, at the risk of being stupid, how long are the base and rise of the triangle for one corner is?

You know, the base dimension and the rise dimension?, for your right triangle in the corner? That is an easy enough set of dimensions...

Then you take that square in inches, and remove that times four from the length and width of your square/rectangle of a spa.

But then, you already knew that Chris...Easiest things first...

v/r

Joshua

I think you just forgot.

Ya know, that ancient indian, Pythagoras, was observing a wrestling match between three lads, observed by their mothers, sitting on a set of animal skins. One lady got quite upset and whomped the other two contestants after they ganged up on her son, and Pythagoras was heard to observe that the squaw on the hippopotamus was equal to the sons of the squaws on the other two hides.

(For a right triangle with 45 degree corners, the base (hypotenuse) is twice the rise, since the rise bisects the triangle into two smaller 45 degree right triangles each with the remaining side (1/2 the base of the original) equal to the rise).

... Bruce (was a math major for too long)

Ya know, that ancient indian, Pythagoras, was observing a wrestling match between three lads, observed by their mothers, sitting on a set of animal skins. One lady got quite upset and whomped the other two contestants after they ganged up on her son, and Pythagoras was heard to observe that the squaw on the hippopotamus was equal to the sons of the squaws on the other two hides.

(For a right triangle with 45 degree corners, the base (hypotenuse) is twice the rise, since the rise bisects the triangle into two smaller 45 degree right triangles each with the remaining side (1/2 the base of the original) equal to the rise).

... Bruce (was a math major for too long)

Yup, times four, and divided by two, and then subracted from the square total, of the "square"...carpenters love squares (just look at me...)