Question

In a right angled triangle the two shorter sides have lengths of (3x + 3) cm and (2x − 1)cm. The hypotenuse has length (5x - 2)cm. Form an equation and solve it to find x.​

Answer 1

x = 3

Step-by-step explanation:

(3x + 3)² + (2x − 1)² = (5x - 2)²

9x² + 18x + 9 + 4x² - 4x + 1 = 25x² - 20x + 4

-12x² + 34x + 6 = 0

6x² - 17x - 3 = 0

(6x + 1)(x - 3) = 0

6x + 1 = 0 or x - 3 = 0

6x = -1 or x = 3

x = -1/6 or x = 3

We discard x = -1/6 because it will make some side lengths negative.

x = 3

Answer 2

To find the value of x in a right-angled triangle, we can use the Pythagorean theorem. By forming and solving an equation, we can determine the possible values of x. x has two values: x = 2 and x = 6/13.

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. The theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. So, we can form an equation as follows:

(3x + 3)^2 + (2x - 1)^2 = (5x - 2)^2

Expanding and simplifying the equation:

9x^2 + 18x + 9 + 4x^2 - 4x + 1 = 25x^2 - 20x + 4

Combine like terms:

13x^2 - 34x + 6 = 0

Now we can solve this quadratic equation to find the value of x. We can use factoring, completing the square, or the quadratic formula to solve it.

After solving the equation, we find that x has two values: x = 2 and x = 6/13.