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

1. ## 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

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

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

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

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

4. ## 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.

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

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

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

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

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

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