The hypotenuse of a right triangle is 2 cm longer than the longer leg. The shorter leg is 23 cm shorter than the longer leg. Find the length of the longer leg of the triangle.

The answer to your question is longer leg = 35 cm

Step-by-step explanation:

Data

hypotenuse = 2cm + longer leg

shorter leg = longer leg - 23 cm

longer leg = ?

Process

1.- Let c be the hypotenuse, a be the longer leg and b be the shorter leg.

2.- Write equations that help to solve this problem

              c = a + 2

              b = a - 23

Pythagorean theorem        c² = a² + b²

3.- Write the equation in terms of a

                                     (a + 2)² = a² + (a - 23)²

4.- Expand

                       a² + 4a + 4 = a² + a² - 46a + 529

5.- Simplify like terms

                       a² + 4a + 4 = 2a² - 46a + 529

                       2a² - 46a + 529 - a² - 4a - 4 = 0

                         a² - 50a + 525 = 0

6.- Factor

                         (a - 35)(a - 15) = 0

7.- Find the value of a

                           a₁ - 35 = 0             a₂ - 15 = 0

                           a₁ = 35                   a₂ = 15

8.- Conclusion

The length of the longer leg is 35. 15 is not possible because we need to subtract 23 from it to find the shorter leg and there are no negative lengths.

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: