Solve each problem using a system of equations in two variable...

Question

Solve each problem using a system of equations in two variables. See Example 6. The longest side of a right triangle is 13 m in length. One of the other sides is 7 m longer than the shortest side. Find the lengths of the two shorter sides of the triangle.

Accepted Answer

Find the length of the two shorter sides of a right triangle whose longest side is 25 centimeters and one of the other two sides 17 centimeters longer than the shortest side. And we have a couple answers here for different side links. Now to solve this, let's first look at what the problem is but the two shorter sides of a right triangle, one of the two sides is 17 centimeters longer. If we know that side, that's why. And our shortest side is X. Our wife should be 70 centimeters longer or X plus 17. Now, to solve this, we can use a substitution in the Pythagorean theorem. The Python theorem states that X squared plus Y squared is equals to the hypotenuse squared. So we have a Y now to X squared plus X plus squared equals a hypo 25 square. We know this is the because it says the longest side is 25 centimeters, we can now simplify X square or X plus 17 square should expand to X squared plus X plus 2, 89. And our 25 squared equal to 6 we then get two X squared plus 34 X plus 2 89 equals 6 25. We once set this equal to zero. So we will move our 6 25 over to get two X squared plus 34 X minus 3, 36 equals zero. Finally, we can divide everything by two to get X squared plus 17, X minus 1 68 equals zero. Now solve for X to find the length of our shortest site. We can use a factor. So we need two numbers that multiply to equal 1 68 and add to equal 17, we have a negative 1 68. So one will be negative and one will be positive. Let's say we choose 24 7. You will see X plus 24 X minus seven equals zero. You can set both of these equals to zero, X plus 24 equals zero, X minus seven equals zero. We get X equals negative 24 X equals positive seven. When moving to the other side. Now we want to take the positive answer only because we can't have a negative length. That means our X is equals to seven. We can now substitute this back into our Y equation. Y equals X plus 17, Y will equal seven plus 17, which means Y is equal to 24. So we have a side of seven centimeters and the other side is centimeters. The answer to our problem then turns out to be uncertainty. Ok. I hope to help you solve the problem. Thank you for watching. Goodbye.

Solve each problem using a system of equations in two variables. See Example 6. The longest side of a right triangle is 13 m in length. One of the other sides is 7 m longer than the shortest side. Find the lengths of the two shorter sides of the triangle.

Key Concepts

Systems of Equations

Pythagorean Theorem

Algebraic Expression of Word Problems

Watch next