Any maths wizards on here help me? pythagoras lol

[richglanzav]

right guys I'm not the best at maths. I'm doing a course for work and it involves work with right angled triangles and Pythagoras theorem with angles, side lengths, areas, etc.

now either I have got this question wrong, or I have unknowingly rewritten the laws of the universe. so I will put below what I have found, and someone feel free to tell me why I am wrong.

we all know the basic right angled triangle. lets call it ABC. triangle ABC has lengths of 3cm, 4cm, and 5cm. so obviously 3 squared = 9, 4 squared = 16 and 5 squared = 25, and the sums of the squares of the two shorter sides = the square of the hypotenuse (longest side) - 16+9=25. that's easy right?

well if you take another triangle with the exact same dimensions but all sides are 1.5 times longer, lets call it DEF. so the sides of this one are 4.5cm, 6cm, and 7.5cm. now for the confusing part (for me). even though essentially this is the same triangle except for the sides are all 1.5 times longer, when I had to work out the ratio in area of the two triangles I found that no matter how much I thought about it, DEF has more than 1.5 times the area of ABC.

Its actually 2.25 times the area unless I'm doing something wrong. How the fuck is this possible? how can making all lengths a certain ratio larger mean that the area of the triangle doesent increase by the same ratio? should I get a nobel prize for creating matter for nothingness?

 

 

 

 

[Calum122]

But you're not increasing the size of the triangle by a factor of 1.5, you're increase the size of each side by a factor of 1.5.

 

Therefore your coefficients are compounded.

The area of a right angled triangle need not be calculated via Pythagoras theorem.

You Simply need 1/2 *x * y, where x is the length of the base and y is the length of the height.

Therefore if your example

 

Your equation expands to (1.5 *(1/2*x)) * (1.5*y)

Therefore you are increasing the size of the triangle by 1.5 * 1.5 = 2.25

 

Plug that back into your original equation 6 * 2.25 = 13.5 which is what you'd expect

I think maybe you're mixing up your theorems a bit here. No Pythagoras was needed to calculate the area.

[5e colin]

1 hour ago, Calum122 said:

But you're not increasing the size of the triangle by a factor of 1.5, you're increase the size of each side by a factor of 1.5.

 

Therefore your coefficients are compounded.

The area of a right angled triangle need not be calculated via Pythagoras theorem.

You Simply need 1/2 *x * y, where x is the length of the base and y is the length of the height.

Therefore if your example

 

Your equation expands to (1.5 *(1/2*x)) * (1.5*y)

Therefore you are increasing the size of the triangle by 1.5 * 1.5 = 2.25

 

Plug that back into your original equation 6 * 2.25 = 13.5 which is what you'd expect

I think maybe you're mixing up your theorems a bit here. No Pythagoras was needed to calculate the area.

 

 

FUCK me i should of stayed in school  fecking Chinese that is 

[richglanzav]

haha dude I think I get it. I am doing the SMC Tech optical technicians course and its all about the reflective and refractive behaviours of light.

I kinda get it - well ive put that as my answer so hopefully it will be marked as correct lol

 

 

 

[Calum122]

Maths is easy, it's arithmetic that's difficult.

Things make more sense when expressed algerbraically.

It's easier to understand why something is when you abstract its behaviour.

It's harder to see this when you're bogged down in the numbers.

The reason it's not 1.5 bigger is because you are multiply both sides by 1.5.

If you want to know what the sides would be when it is 1.5 times bigger, you must work backwards.