Thread: Quadratics

The question:

In a right angled triangle the second to longest side is 5cm longer than the shortest and the hypotenuse is 3 times longer than the shortest side. Find the exaact length of the hypotenuse.

The answer is (15+30 root2)/7

But I got this 5+root50 through the following working:
Could you please tell me where I went wrong?

The right hand side should be

umm why?

Because both the 3 and x have to be squared:



Then solve using the quadratic formula.


01

Your working should be something like this

a² + b² = c²
(x)²+ (5+x)² = (3x)²
x² + 25 + 10x + x² = 9x²
2x² +10x + 25 =9x²
7x²- 10x -25 = 0

Use quad formula from here to get answer.

Oh could you tell me how I messed up in the quadratic formula then?



^ My answer is (5+/- 10root2)/7 rather than ( 5+/- 30root2 )/7

7x²-10x-25=0

Using quad

= -(-10) + root of (-10)² - 4 (7) (-25)
Divided by 2(7)

=10 + root of 100 + 700
divided by 14

Firstly:
why is it 100-700 --> -4 * 7 *-25 should be positive since there are two negatives multiplying against one another

Secondly:
if it is 100-700 then it will be a NEGATIVE number which cannot square root and therefore the answer will be "no real solutions" which is even more incorrect

Um how did you get that?

Hmm, I'm not getting the original answer. I'm getting what prettiestfriend got.


01