Answer:
Explanation:
To find the value of x, we can use the information given in the problem. We have AB = 4x and BC = 2x + 8.
Using the Pythagorean theorem, we can find the length of AC. The theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
So, AC^2 = AB^2 + BC^2.
Substituting the values, we get:
AC^2 = (4x)^2 + (2x + 8)^2.
Expanding the squares, we get:
AC^2 = 16x^2 + 16x^2 + 64x + 64.
Combining like terms, we get:
AC^2 = 32x^2 + 64x + 64.
Solving for x, we can use the information that AB = 14 inches. So, 4x = 14 and x = 3.5.
Now that we have the value of x, we can find the lengths of AB, BC, and AC.
AB = 4x = 4 * 3.5 = 14 inches
BC = 2x + 8 = 2 * 3.5 + 8 = 13 inches
And finally, using the Pythagorean theorem, we can find the length of AC:
AC = √(32x^2 + 64x + 64) = √(32 * 3.5^2 + 64 * 3.5 + 64) = √(588).
So, the length of AC is approximately 24.33 inches.
The final answer is x = 3.5, AB = 14 inches, BC = 13 inches, and AC = 24.33 inches.