Answer each question. Sides of a Right TriangleTo solve for th...

Question

Answer each question. Sides of a Right TriangleTo solve for the lengths of the right triangle sides, which equation is correct?

Right triangle with legs labeled x and x+4, and hypotenuse labeled 2x-2, showing a right angle.

A. x^2=(2x-2)^2+(x+4)^2 B. x^2+(x+4)^2=(2x-2)^2 C. x^2=(2x-2)^2-(x+4)^2 D. x^2+(2x-2)^2=(x+4)^2

Accepted Answer

Hello, everybody. I hope you're doing all right. Today, we're going to be looking at this question that states which of the following equations represents the sides of a triangle given below where our triangle looks like a right triangle with one side being labeled as X, another side being labeled as three, X minus three. And the hypo being labeled as as X plus nine. Now, our choices are A X squared equals open parentheses. Three X minus two closed parentheses squared plus open parentheses, X plus nine, close parentheses squared, B X squared plus open parentheses. Three, X minus three closed parentheses, squared equals open parentheses, X plus nine, closed parentheses, squared, C X squared equals open parentheses, three, X minus three, closed parentheses, squared minus open parentheses, X plus nine, closed parentheses. Squared N D X squared plus open parentheses, X plus nine closed parentheses squared equals open parentheses. Three, X minus three, closed parentheses squared. Now, to write the equation of a right triangle specifically, we should note uh of so what is this theorem? Well, the general rule theorem is that A squared plus B squared equals C squared where A M B R the non hypos sides and see is the hypos. So in this case, I'll just assign A to be the side of X B will be the side of three X minus three and C will be the hypotenuse of X plus nine. So plugging that in to our A squared plus B squared equals C squared, we'll have A, in this case. So we'll have X squared plus B squared. So our, our B was three, X minus three, I'll have all of that squared now and that equals C squared and our C was X plus nine. So I'll have X plus nine instead of a parentheses and squared that parentheses. So now I can go ahead and square this to have that X squared is equal to nine X squared or actually, we can leave it. We don't have to continue to simplify. If we look at our answers, we can leave it in this form and simply compare this to the answers provided. So we have X squared plus open parentheses, three, X minus three, closed parentheses squared. And that'll be equal to open parentheses, X plus nine, close parentheses squared. So now we can just look at the answers that they provided us and see that answer choice B matches with this equation. So theoretically, you can go ahead and distribute all the squares and such. But for this question, we don't have to go ahead and do that and we can go ahead and pick answer choice B as the right answer for this question. So I hope that was helpful and until next time.

Answer each question. Sides of a Right TriangleTo solve for the lengths of the right triangle sides, which equation is correct?

A. x^2=(2x-2)^2+(x+4)^2 B. x^2+(x+4)^2=(2x-2)^2 C. x^2=(2x-2)^2-(x+4)^2 D. x^2+(2x-2)^2=(x+4)^2

Key Concepts

Pythagorean Theorem

Identifying the Hypotenuse

Forming Equations from Triangle Sides

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