Question

10:51

HW 1 Pythagorean Theorem and its Converse
3 of 4
8.
10
28
25
x
What is the value of x?
√59
√629
16.1
22.9
...
iii
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Answer 1

The value of x is
`√(59)` using Pythagorean Theorem and its Converse. Option a is the correct choice.

To find the length of the hypotenuse AC in a right-angled triangle ABC given the base AB and height BC, you can use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the lengths of the other two sides (AB and BC).

The Pythagorean Theorem can be written as:

`\[ AC^2 = AB^2 + BC^2 \]`

In your case, AB = 10 and BC = 25, so you can substitute these values into the formula:

`\[ AC^2 = 10^2 + 25^2 \]`

`\[ AC^2 = 100 + 625 \]`

`\[ AC^2 = 725 \]`

Now, to find AC, take the square root of both sides:

`\[ AC = √(725) \]`

`\[ AC \approx 26.91 \]`

Therefore, the length of the hypotenuse AC is approximately 26.91.

To find the length of the side DB in a right-angled triangle ADC given the height AC and hypotenuse DA, you can use the Pythagorean Theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (DA) is equal to the sum of the squares of the lengths of the other two sides AC and (DB).

The Pythagorean Theorem can be written as:

`\[ DA^2 = AC^2 + DB^2 \]`

In your case, AC = 26.91 and DA = 28, so you can substitute these values into the formula:

`\[ 28^2 = 26.91^2 + DB^2 \]`

`\[ 784 = 724.2081 + DB^2 \]`

Now, solve for
`\(DB^2\)`:

`\[ DB^2 = 784 - 724.2081 \]`

`\[ DB^2 = 59.7919 \]`

Now, take the square root of both sides to find DB:

`\[ DB = √(59.7919) \]`

`\[ DB \approx 7.73 \]`

Therefore, the length of the side DB is approximately
`\(7.73\)`.
Option a is the correct choice.