Math CentralQuandaries & Queries


I know the hypotenuse of a right triangle is a^2 + b^2 = c^2 but when
I replace this with the numbers given, I can't solve it.

Here is my question: The hypotenuse of a right triangle is 2.8 units
long. The longer leg is 1.9 units longer than the shorter leg. Find
the lengths of the sides of the triangle.

My choices are:

2.8, 0.9, 2.8

0.6, 2.5, 2.8

2.8, 1.9, 4.6

2.8, 2.7, 0.8

Hi Sharon,
You have two options of how to solve this question. The first is to just plug each of your choices into the Pythagorean theorem and see which one works. The only problem is the answers have been rounded, so it won't work out perfectly. You can rule out two of the choices right away, as the hypotenuse must be the longest side of the triangle, so there can't be another side that is 2.8 or a side that is 4.6.

The other option is to set up the pythagorean theorem with variables and solve for x. If you choose this method, we know that the hypotenuse is 2.8 units. Then we can let the shorter leg be x, which would make the longer leg be x + 1.9. I solved it using the quadratic formula and rounded my final answer to the nearest tenth, which is one of your solutions. Good luck.


Hi Sharon,

Pam is correct that you can remove two of the choices immediately. In fact look at the choices again. You know that two of the sides have lengths 2.8 units and 1.9 units. Only one of the choices has these two numbers as side lengths, but this is one that Pam ruled out. The correct answer is not in the list of choices. The way to find the correct answer is to use the second method suggested by Pam.


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