SOLUTION: The hypotenuse of a right angled triangle exceeds one side by 1cm and the other side by 18cm,Calculate the length of the shortest side?

Question 967811: The hypotenuse of a right angled triangle exceeds one side by 1cm and the other side by 18cm,Calculate the length of the shortest side?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!

Let x be the length of the hypotenuse of the given right angled triangle.

Then the length of one leg is x-1, and the length of the other leg is x-18, according to the condition.

Then the Pythagorean theorems gives an equation
+ = .

Simplify and solve it step by step to find x.

+ = ,

= ,

= = = = .

= = = = .

Thus there are two solutions for the hypotenuse: 25 units and/or 13 units. Since one leg is 18 units shorter than the hypotenuse, only one solution has sense: x = 25.

Answer. The hypotenuse is 25 units long. The legs are of 24 and 7 units long. The shortest side is of 7 units long.

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