The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

Hi guys,

Question: The lengths of the sides of a right angled triangle are $\displaystyle (2x+1)$ cm, $\displaystyle 6x$cm and $\displaystyle (5x+3)$ cm. Calculate the value of x and hence find the area of the triangle

I tried using Pythagoras Theorem but if I were to expand the algebra given, the answers would be completely different? How should I go around to solve it?

Thanks

Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

Quote:

Originally Posted by

**FailInMaths** Hi guys,

Question: The lengths of the sides of a right angled triangle are $\displaystyle (2x+1)$ cm, $\displaystyle 6x$cm and $\displaystyle (5x+3)$ cm. Calculate the value of x and hence find the area of the triangle

I tried using Pythagoras Theorem but if I were to expand the algebra given, the answers would be completely different? How should I go around to solve it?

Thanks

There are two possibilities for the hypotenuse that you need to consider the 6x and the 5x+3 these could both be the hypotenuse, 6x if x>3 and 5x+3 if x<3.

You need to look at both of these cases.

CB

Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

Quote:

Originally Posted by

**CaptainBlack** There are two possibilities for the hypotenuse that you need to consider the 6x and the 5x+3 these could both be the hypotenuse, 6x if x>3 and 5x+3 if x<3.

You need to look at both of these cases.

CB

Hmm, the answer stated here is 2. Can I assume that this question is unclear? I mean, like what you said, there are 2 hypotenuse

Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

If the answer is 2 then consider like CB has said $\displaystyle 5x+3$ as the hypothenuse, that means if we use Phytagoras theorem:

$\displaystyle (5x+3)^2=(6x)^2+(2x+1)^2$

Solve this equation.

Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

Quote:

Originally Posted by

**Siron** If the answer is 2 then consider like CB has said $\displaystyle 5x+3$ as the hypothenuse, that means if we use Phytagoras theorem:

$\displaystyle (5x+3)^2=(6x)^2+(2x+1)^2$

Solve this equation.

Yeah, but I think the question itself is unclear. Without the answer, how would we have know that (5x+3) is the hypotenuse

Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

Quote:

Originally Posted by

**FailInMaths** Yeah, but I think the question itself is unclear. Without the answer, how would we have know that (5x+3) is the hypotenuse

By doing the calculations in both cases, you will find only one solution consistent with x>0 and x<3 for the 6x hypotenuse and x>3 for the 5x+3 hypotenuse.

So you compute all four solutions and only one is consistent with the constraints.

CB

Re: The lengths of the sides of a right angled triangle are.... (Pythagoras Theorem)?

Quote:

Originally Posted by

**CaptainBlack** By doing the calculations in both cases, you will find only one solution consistent with x>0 and x<3 for the 6x hypotenuse and x>3 for the 5x+3 hypotenuse.

So you compute all four solutions and only one is consistent with the constraints.

CB

Ok, I get it now, thanks