The longer leg of a right triangle is 1 ft longer than the shorter leg. The hypotenuse is 1 ft shorter than twice the shorter leg. Find the length of the shorter leg of the triangle.

Question

The longer leg of a right triangle is 1 ft longer than the shorter leg.  The          hypotenuse is 1 ft shorter than twice the shorter leg.  Find the length of the         shorter leg of the triangle.

anonymous · Answer

one leg x, the other is x + 1 and the hypotenuse is 2(x-1) now pythathatoas

anonymous · Answer

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

anonymous · Answer

$$x^2+x^2+2x+1=4(x^2-2x+1)$$
$$2x^2+2x+1=4x^2-8x+4$$
$$2x^2-10x+3=0$$

anonymous · Answer

oh damn i did it wrong! says  hypotenuse is 1 ft shorter than twice the shorter leg so it should be 2x-1 i start again

anonymous · Answer

$$x^2+(x+1)^2=(2x-1)^2
$$$$2x^2+2x+1=4x^2-4x+1$$
$$2x^2-6x=0$$
$$2x(x-3)=0$$ so x = 0 which is silly, or x = 3 which gives a nice 3 - 4 - 5  right triangle which we could have guessed from the beginning

anonymous · Answer

I get it thank you for your help