Question

Grade 10 Math- Quadratic Equations

Please help! I have a test tomorrow and don't understand how to do this question on the review. I think I drew the diagram correct but I don't know what to do after I put all the values into the formula.

The length of the hypotenuse of a right triangle is 1 cm more than triple that of the shorter leg. The length of the longer leg is 1 cm less than triple that of the shorter legm Find the lengths of the three sides of the triangle.

Answer 1

If you plug the values for a, b, and c into the Pythagorean Theorem, you can get x alone to figure out the side lengths:

x² + 3x² - 1² = 3x² + 1²
Combine like terms
4x² - 1² = 3x² + 1²
Subtract 3x² from both sides
x² - 1² = 1²
Simplify 1²
x² - 1 = 1
Add 1 to both sides
x² = 2
Square root both sides
x = 1.41421

Then, simply plug in that number for x on each side! It comes out to a weird number, but I don't see any other way to solve it...
Hope this helps :)