The answer, in short, is that the short leg equals 15 mm, the long leg equals 20 mm, and the hypotenuse equals 25mm. but if you'd like to see how I solved it, here are the steps. ----------------------------- The Pythagorean theorem (also known as Pythagoras's Theorem) can be used to solve this. This theorem states that one leg or a right triangle squared plus the other side of that same triangle squared equals the hypotenuse of that triangle squared. To put it in equation form, L² + L² = H².
Let's call the longer leg B, the shorter leg A, and the hypotenuse H. From the question, we know that A = B - 5, and H = B + 5.
So if we put those values into an equation, we have (B - 5)² + B² = (B + 5)²
Now, to solve. Let's square the two terms in parentheses first: (B² - 5B - 5B + 25) + B² = B² + 5B + 5B + 25
Now combine like terms: 2B² -10B + 25 = B² + 10B + 25
And now we simplify. Subtract 25 from each side: 2B² - 10B = B² + 10B
Subtract B² from each side: B² - 10B = 10B
Add 10B to each side: B² = 20B
And finally, divide each side by B: B = 20
So that's the length of B. Now to find out A and H. A = B - 5, so A = 15. H = B + 5, so H = 25.
And your final answer is A = 15mm, B = 20mm, and H = 25mm
