Question

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.

Answer 1

25cm

Explanation:

First I named the sides, like in the picture. The longest leg is x, the hypothenuse is x+2, the shortest leg is x-23. Then you can use pythagorean theorem to solve for x. You're left with a quadratic equation, which can be solved by factorization, like in the attatchment below. Once you solve it, you get two answers, 21 and 25, but 25 is the answer since 21 is too small. If you subtract 23 from 21, you're left with a negative number, which is impossible. I hope this helped you!

Answer 2

The answer to your question is longer leg = 35 cm

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.