SOLUTION: The length of the shortest side of a right triangle is 11 inches. The lengths of the other two sides are represented by consecutive integers. Find an equation to find the lengths o

Algebra ->  Triangles -> SOLUTION: The length of the shortest side of a right triangle is 11 inches. The lengths of the other two sides are represented by consecutive integers. Find an equation to find the lengths o      Log On


   

Question 1117552: The length of the shortest side of a right triangle is 11 inches. The lengths of the other two sides are represented by consecutive integers. Find an equation to find the lengths of the other sides.
How do we find this equation?
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
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The shortest side of the length 11 inches is the shorter leg.


Let x be the length of the longer leg (x > 11).

Then the length of the hypotenuse is (x+1) inches - it is the longest side of the triangle.


Then the Pythagorean theorem gives you an equation


11%5E2 + x%5E2 = %28x%2B1%29%5E2.


Simplify and solve it:

121 + x%5E2 = x%5E2+%2B+2x+%2B+1,

121 = 2x + 1,

120 = 2x  ====>  x = 120%2F2 = 60.


Answer.  The longer leg is 60 inches long.  The hypotenuse is 61 inches long.


Check.  60%5E2 + 11%5E2 = 3721 = 61%5E2.


        The triangle inequalities for such segments are satisfied, too; so the solution is correct !