the hypotenus if a right triangle is 6 meters long. One leg is one meter longer than the other find the legth of the shorter leg. round to the nearest hundred.

Question

ash2326 · Answer

Let one leg be x , so the other one will be x-1, we have this
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trevino do you know Pythagoras theorem??

anonymous · Answer

yes a^2 + b^2 =c^2

ash2326 · Answer

yeah, now we have
$$x^2+(x-1)^2=6^2$$
let's expand the brackets
$$x^2+x^2-2x+1=36$$
we get now
$$2x^2-2x-35=0$$
Can you solve now??

anonymous · Answer

so i would now use $$-b \pm \sqrt{b ^{2}-4(a)(c)}$$

anonymous · Answer

divided by 2a

ash2326 · Answer

yeah use it, you'd get two values of x, find and tell me

anonymous · Answer

k one sec

anonymous · Answer

i got 4.713 and -3.713

ash2326 · Answer

you're correct , take the positive value
x=4.71
x-1=3.71

anonymous · Answer

so the answer since we are lookin for the smallest one would be 3.71

anonymous · Answer

3.713

ash2326 · Answer

no, one leg is 4.713 and the other one is 3.713

anonymous · Answer

but it wants the legth of the shortest leg so it would be 3.713 right?

ash2326 · Answer

we have to find both the legs, have to solve the triangle

anonymous · Answer

so c^s - b^2 = a^2

ash2326 · Answer

No, we have c=6
a=x
b=x-1
so
$$x^2+(x-1)^2=6$$
we found x from this quadratic equation.
So x and x-1 are the two sides of the right triangle