Question 851082
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The hypotenuse of a right triangle is 75 inches long. One leg is 5 inch(es) longer than the other. Find the lengths of the legs of the triangle. Round your answers to the nearest tenth of an inch.
Solution:
Let the shortest side be x
Then the second side is x + 5
And the hypotenuse is 75 in. long.

Applying Pythagoras theorem,
{{{x^2 + (x + 5)^2 = 75^2}}}
{{{x^2 + x^2 + 10*x + 25 = 5625}}}
i.e. {{{2*x^2 + 10*x - 5600 = 0}}} or Dividing it by 2 throughout
{{{x^2 + 5*x - 2800 = 0}}}
This can be solved using the quadratic solver as shown below.

*[invoke quadratic "x", 1, 5, -2800 ]

The solution is the positive value of x is 50.5 inches (rounded off), since the length of a side cannot be negative.

So the lengths of the sides are {{{highlight(50.5)}}}, {{{highlight(55.5)}}}, and {{{highlight(75)}}} inches respectively.

:)

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