Question

Find an integer, x, such that 2, 4, and x represent the lengths of the sides of an acute triangle.

Answer 1

x≤ 2 I think

Answer 2

Is there a diagram? Is there angles? So it's not a right angled triangle?

Answer 3

For an acute angled triangle
a^2 < b^2 + c^2

where a,b and c are the sides of the triangle a being the longest side

Answer 4

What theorm is that cwrw238? :)

Answer 5

for sides 2,4 and x
x must obviously be > 2

must also
x ^2 < 2^2 + 4^2
x^2 < 20
x < sqrt20

Answer 6

so for x to be an integer it must be 3 or 4

Answer 7

I dont now if theres a name to that theorem

for a right angled triangle a^2 = b^2 + c^2
obtuse traingle a^2 > b^2 + c^2
acute triangle a^2 < b^2 +c ^2

Answer 8

I thought for a right angled triangle it's c^2 = a^2 + b^2? (Where c = hypotenuse)?

Answer 9

When do you learn about obtuse and acute, and in what subject - Geometry? (When like grade/year level)?

Answer 10

the order doesn't matter the hypotenuse can be a, b or c Though its more usual to call it c.

Answer 11

Yes in geometry - not sure what grade/ year if you mean the American system. In UK it would be at age of about 13/14

Answer 12

Thanks so much cwrw238, much appreciated! :) I'm excited to research more about this~ <3