SOLUTION: Find the length of the hypontenuse of a right-angled triangle whose sides are x cm, (X + 1) cm and (X + 3) cm

Algebra ->  Pythagorean-theorem -> SOLUTION: Find the length of the hypontenuse of a right-angled triangle whose sides are x cm, (X + 1) cm and (X + 3) cm      Log On


   



Question 814781: Find the length of the hypontenuse of a right-angled triangle whose sides are x cm, (X + 1) cm and (X + 3) cm
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+%28x%2B1%29%5E2+=+%28x%2B3%29%5E2
=
x%5E2+%2B+x%5E2+%2B+2x+%2B1+=+x%5E2+%2B+6x+%2B+9
2x%5E2+%2B+2x+%2B+1+=+x%5E2+%2B+6x+%2B+9
Now subtract x%5E2+%2B+6x+%2B+9 from
each side.
x%5E2+-+4x+-+8+=+0+
= x%5E2+-+4x+=+8+
Completing the square
x%5E2+-+4x+%2B+4+=+8+%2B+4+
%28x+-+2%29%5E2++=+12+
x+-+2++=+%2B-sqrt%2812%29+
x+++=+2+%2Bsqrt%2812%29+ or x+++=+2+-+sqrt%2812%29+
Only the first value is positive, so
since the hypotenuse is x+3 = 2+%2Bsqrt%2812%29%2B+3+
= 5+%2Bsqrt%2812%29+ = 5+%2B2%2Asqrt%283%29+