Question

If a(3,-3) and b(x,-3) and C( 9, 4) are vertices of a right triangle with AC, being the longest side. Also, x > 5, is greater than, 5. Find x​

Answer 1

To find the value of x, we can use the Pythagorean theorem. Given that AC is the longest side of the right triangle, we can set up an equation and solve for x.

Step-by-step explanation:

To determine the value of x, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, AC is the hypotenuse, and AB and BC are the other two sides.

Given that AC is the longest side, we can use this information to find the value of x:

AB^2 + BC^2 = AC^2

(3 - x)^2 + (-3 - (-3))^2 = (9 - 3)^2

9 - 6x + x^2 + 0^2 = 36

x^2 - 6x - 27 = 0

Using the quadratic equation, we can solve for x:

x = (-(-6) ± √((-6)^2 - 4(1)(-27)))/(2(1))

x = (6 ± √(36 + 108))/(2)

x = (6 ± √(144))/(2)

x = (6 ± 12)/(2)

x = (6 + 12)/(2) or x = (6 - 12)/(2)

x = 18/2 or x = -6/2

x = 9 or x = -3

Since x > 5, the solution is x = 9.