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if the length of the base of an isosceles right triangle is 2, what is the length of each congruent leg?

hint: remember, the base of an isosceles triangle is the third side-not one of the equal sides. even though you're just given one side, you can set up an equation using the pythagorean theorem and solve (because two of the sides are equal).

If you are not familiar with the Pythagorean theorem, I will write it below to remind you for your future mathmatical endeavours:



c is the hypotenuse, and a and b are the other two sides. The hypotenuse is the largest side of a triangle. In this example, a and b are equal to each other and c is equal to 2, so I'm going to convert b into a and do some math trickery here:





Basically, I swapped b with a and combined like terms. Then I just replaced c with 2, then squared it into 4.

All you have to do now is solve for a

Step 1 is to divide both sides by 2 to get:



Then just square both sides:



Now you know that the length of the sides are equal to the square root of 2.

Sorry if this was a bit rushed, I hate running out of time on these. If you have any questions on why I did something, ask away in the comments.

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