Right angle triangle word problem.?

Question

The hypotenuse of a right triangle is 13 cm. If one leg is 2 cm. more than twice the other leg, find the length of the legs.

If someone were to just show me what the initial setup might be, I could then solve this problem. But every approach I've taken so far (e.g. (13)^2 = (2x)^2 + (x + 2)^2, and the like) has led to no avail.

Thank you in advance.

Answer 1

took me awhiles to figure out why the trinomial was not whats the word whereu put it into 2 sets.  It's been 5 years since i've done algebra.  Well i've figured out your mistake.  

the equation you gave doesn't have a single constant.  I at first also thought that equation was right, so i wont deny that first equation was a fair mistake.

Your equation has 3  different parts when you need 2.  It's hard for me to explain.  I guess the easiest way to put it is in your first equation you have let one side be 2x^2 and another one be (x+2)^2 but you have no reference to what the orginal x was, which would total 3 diff lengths(beyond the hypotenuse)

Any ways here is a simple way to look at it.  Since the first ("one") leg is the one that is different than the second leg ("other") leg lets let x = the other leg

let x = the other leg

let 2x +2= the one leg

169= x^2  + (2x+2)^2

169 = X^2 + 4X^2 +8X +4

169= 5X^2 +8X +4

0 = 5X^2 +8X -165

to skip trial and errors with all the factors of 165 I'll just type in this thing factored out

0= (5x +33) (x-5)

so we have to possible answers since if either ( ) ='s 0 the equation will be true.

5x+33=0

5x=-33  

x= -33/5 (x can't be less than 0 since there are no negative measurements so this one is wrong)

x-5 = 0

x=5

so you answer is 5

one side is 5 the other side is12 ( 2 x 5 +2)

25 + 144 = 169 (13squared)

Answer 2

13^2=x^2+(2x+2)^2

(2x+2)^2=(2x+2)(2x+2)=4x^2+8x+4, and 13^2=169, thus

169=x^2+4x^2+8x+4=5x^2+8x+4 (adding like terms)

subtract 169 from both sides 0=5x^2+8x-165

use the quadratic equation to get zero's at 5 and -6.6, since we can't have a negative length, we know the 5 is right for one of the legs

the other leg is 2(5)+2=12

check 13^2=5^2+12^2

            169=25+144

so we're good

Answer 3

h² = a² + b²

13² = x² + (2x+2)²

169 = x² + (4x² + 8x + 4)

169 = x² + 4x² + 8x + 4

000 = x² + 4x² + 8x - 165

000 = 5x² + 8x - 165

There are two real number roots.

x1 = 5

x2 = -6.6

It can't be negative, so one leg is 5 and the other is 2(5)+2=12

Plug the numbers in to check:

13^2=5^2+12^2

169=25+144

That's it!  The legs are 5 and 12.

Answer 4

For a right triangle, the formula to use would be the Pythagorean Theorem which is c^2=a^2+b^2. c is the hypotenuse and a and b both stand for each leg.

substitute...13^2=2+(2b^2)+b^2

continue solving...169=2+(2b^2)+b^2

and so on...