Question 1031354
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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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Leg        :: x
Hypotenuse :: x + 1
Other leg  :: 7.

Pythagorean equation:

{{{x^2 + 7^2}}} = {{{(x+1)^2}}}.

{{{x^2 + 49}}} = {{{x^2 + 2x + 1}}},

{{{49}}} = {{{2x+1}}},

2x = 48,

x = {{{48/2}}} = 24.

<U>Answer</U>.  Two legs are 24 and 7 units long. The hypotenuse is 25 units long.

<U>Check</U>. {{{24^2 + 7^2}}} = 625 = {{{25^2}}}.
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