Right triangle?

Question

One leg of a right triangle is 1 cm longer than the other leg. What is the length of the short lef if the total length of the hypotenuse and the short leg is 10 cm?

I solved the equation, but I get a decimal number. Did I solve it right?

Answer 1

short leg = s
long leg = s + 1
hypotenuse = sqrt(s^2 + (s+1)^2)
10 = s + sqrt(2s^2+2s+1)
solve the quadratic equatyon to get
s^2 - 20s + 100 = 2s^2 +2s+1
s^2+22s-99 = 0
solution: s = (-22 + sqrt(484 + 396)) /2 = -11 + sqrt(220) =3.8324...

Answer 2

Following are relations you can apply to problem you have stated.

1) In a zero start 2D square matrix (a usual graphics software does apply it) you can take any merged yx position as (y-x)=1 (or (x-y)=1), like 43 or 34! you are aware that 3^2+4^2= 5^2 and 5+3 =8 which is nearest whole number state of your problem!

2) A related rule is, take any odd number, then square it and equally split it and make these answers as one unit difference like, 5^2= 25---> 12.5 and 12.5 ----> 12 and 13.
Then 13^2- 12^2= 5^2. Mattars like these are with in mental computing range! Though it could be applied to any odd number your problem is nearest to explanation (1)

3) No other right triangle having 'a-unit difference between long and short legs' have a-unit step hypotonuse( they are decimal values)

4) If you manage to keep hypotonuse a-unit step then both legs are decimal values!

5) Conditions (3) and (4) together indicate that if your formula is correct you will get a decimal value alone as you have stated!

Answer 3

Short leg = x
Long leg = x+1
Hypotenuse = 10 - x

x^2 + (x+1)^2 = (10-x)^2

x^2 + x^2 + 2x + 1 = 100 - 20x + x^2

x^2 + 22x - 99 = 0

This does not factor using integers, so yes the answer is a decimal.

Answer 4

One leg = x, second leg = x+1, hypotenuese = 10-x

use pythagoras:
a^2 + b^2 = c^2
x^2 +(x+1)^2 = (10-x)^2
multiply out
x^2 + x^2 + 2x +1 = 100 - 20x + x^2
group together and set to 0
x^2 + 22x - 99 = 0

use the quadratic formula to solve...
x = -b +/-sqrt(b^2 - 4ac) / 2a
I'm not writing that out...
x = 3.83 is the only positive value.

Check with orginal equations.
x = 3.83
x+1 = 4.83

x^2 + (x+1)^2 = 3.83^2 + 4.83^2 = 38

10-x = 10-3.83 = 6.17.
6.17^2 = 38.1

checks out with a small rounding error.
x = 3.83

Answer 5

One leg: x+1
Short leg: x
Hypotenuse: 10 -x
x^2 + (x+1)^2 = (10-x)^2
x^2 + x^2 + 1 + 2x^2 = 100 - 20x + x^2
4x^2+1 = 100 - 20x + x^2
3x^2 -99 + 20x = 0
x is a decimal.

Answer 6

leg = x
other leg = x+1
hyp = 10 - x

Pythagorean thm.

(10-x)^2 = x^2 + (x+1)^2

100 - 20x + x^2 = x^2 + x^2 + 2x + 1

x^2 + 22x - 99 = 0

x^2 + 22x + 121 = 99 + 121
(x + 11)^2 = 220

x = -11 + sqrt 220 = -11 + 14.8 = 3.8

Answer 7

Yes, it should be a decimal number.

the short leg should be 4.5 and the long leg should be 5.5. thus the total length = 10.

Answer 8

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Answer 9

If your answer makes all these true, then it is correct:

a^2 + b^2 = c^2

a = b -1

a + c = 10

Answer 10

hahaha this is a hard one!!!! I tryed to figure it out and i couldnt get it???? Well wat is it?? is there a way u can tell me....lol...well byez!! -gEoRgIa_lOvE04