In triangle ABC m

Question

In triangle ABC m<C=90 degrees and the length of the hypotenuse is 10. If one leg is twice as long as the other leg, find the length of the shorter leg. Express answer as a simplified square root

cwrw238 · Answer

let x be length of shorter leg, then longer leg = 2x
now apply the pythagoras theorem and solve the equation for x

anonymous · Answer

so would I set up the equation 2x^2+x^2=10^2

cwrw238 · Answer

not quite right - its (2x)^2 =  4x^2
so its

4x^2 + x^2 = 10^2

anonymous · Answer

would the answer be x=+or- 2 square root of 5

cwrw238 · Answer

5x^2 = 100
x^2 = 20
x = sqrt20  = 2sqrt5

- only the positive number is valid as its a length of a side

anonymous · Answer

or so I cannot have negative in this equation. I got it. I appreciate you help

anonymous · Answer

your help

cwrw238 · Answer

nope - you can't have a negative line

cwrw238 · Answer

one solution of the equation is negative - thats correct - but the positive one is the only solution valid in this case