How do you find the lengths of the sides of a right triangle given the legs x and x+1 and the hypotenuse 7?

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Answer 1 · 2016-07-01T15:32:42

Legs of the triangle are 4.424 and 5.524

Write an equation using Pythagoras' Theorem.

#x^2 + (x+1)^2 = 7^2#
#x^2 + x^2 +2x+1 - 49 = 0#

#2x^2 +2x -48 = 0 " " ÷2#

#x^2 +x -24 =0#

#x^2 +x + (1/2)^2 =24 +(1/2)^2#
#(x + 1/2)^2 = 24+ 1/4#

#x + 1/2 = +-sqrt(97/4)#
#x = (+sqrt97)/2 - 1/2" or "x = (-sqrt97)/2 - 1/2#

#x= 4.424 " or " x= -5.424 # (reject as a side)

Legs of the triangle are 4.424 and 5.524