SOLUTION: Suppose one leg and the hypotenuse of a right triangle are consecutive integers. Find the length of the leg and hypotenuse if the other leg is of length 7cm.

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Question 1031354: Suppose one leg and the hypotenuse of a right triangle are consecutive integers. Find the length of the leg and hypotenuse if the other leg is of length 7cm.
Found 3 solutions by stanbon, ikleyn, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Suppose one leg and the hypotenuse of a right triangle are consecutive integers. Find the length of the leg and hypotenuse if the other leg is of length 7cm.
------
leg:: x
hypot:: 2x
leg:: 7 cm
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(2x)^2 = x^2 + 49
3x^2 = 49
x^2 = 49/3
x = 7/sqrt(3) = (7/3)sqrt(3) cm
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Cheers,
Stan H.
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Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Suppose one leg and the hypotenuse of a right triangle are consecutive integers. Find the length of the leg and hypotenuse if the other leg is of length 7cm.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Leg        :: x
Hypotenuse :: x + 1
Other leg  :: 7.

Pythagorean equation:

 = .

 = ,

 = ,

2x = 48,

x =  = 24.

Answer.  Two legs are 24 and 7 units long. The hypotenuse is 25 units long.

Check.  = 625 = .


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Suppose one leg and the hypotenuse of a right triangle are consecutive integers. Find the length of the leg and hypotenuse if the other leg is of length 7cm.
Unknown leg: 

Hypotenuse:   

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