Geometry. DS

There is a brilliant rule

Let the sides of the triangle be a,b and c. And assume that c is the longes side.

Here is the rule:

If c^2>a^2+b^2, then the triangle is obtuse angles (in other words x>90)

If c^2=a^2+b^2, the the triangle is right angled (x=90)

If c^2<a^2+b^2, the the triangle is acute angled (x<90)

So from both statements you can see that c^2>a^2+b^2 => x>90 SUFF.

Tthanks ...yeah i got ...

I can see how option 1 (a^2+b^2<15) can tell us that this x>90, but how does option 2 (c>4) tell us anything?

Thanks

ELYAC Realty wrote:I can see how option 1 (a^2+b^2<15) can tell us that this x>90, but how does option 2 (c>4) tell us anything?

Thanks

I didn't understand where got x>90 from option (a^2+b^2<15). It's insuff.

We must compare c^2 with a^2+b^2
Since c>4 => c^2>16 and a^2+b^2<15
Now at any value of a,b and c in above mentioned inequality c^2>a^2+b^2

From this two statements you can conclude that x>90

ELYAC Realty wrote:I can see how option 1 (a^2+b^2<15) can tell us that this x>90, but how does option 2 (c>4) tell us anything?

Thanks

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Well, I think the first statement is saying that a^2 + b^2 together is smaller than 15, but we dont know the value of 'c' in this statement. Option 2 provides us with the value of 'c'. 'c' is more than 4. therefore, if it is 5, and we square that number, it is 25. now 25>a^2 + b^2.

In conclusion, option 2 tells us the value of C.

Here is the rule:

If c^2>a^2+b^2, then the triangle is obtuse angles (in other words x>90)


So just based of this rule, even though we see c^2 greater than the other two, we shouldn't assume its greater than 90 degrees unless we see what the values are.

In this case, C^2 = 15, so C=3.873. So doesnt that automatically tell us that C is going to be greater than 3.873 satisfying the equation of a^2+b^2<15?

Thanks