The shortest side AB of a right-angled triangle is x cm long. The side BC is
1 cm longer than AB and the hypotenuse, AC, is 29 cm long.
Form an equation for x and solve it to find the lengths of the three sides of
the triangle.
please give full steps
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Answer:
x = 20 cm
Step-by-step explanation:
AB=x cm
BC=x+1 cm
AC=29 cm
(AB)^2 + (BC)^2 = (AC)^2 =
(x)^2 + (x+1)^2 = (29)^2 =
x^2 + x^2 + 2x + 1 = 841 =
2x^2 + 2x + 1 = 841 =
2x^2 + 2x - 840 = 0 =
2x^2 + 42x - 40x -840 = 0 =
2x (x + 12) -40 (x + 12) = 0 =
(2x - 40)(x +12)
x= 20 or x= -12
the number can only be positive so x is 20
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