Question

Homework 1:Pythagorean Theorem and it’s Converse

Find The Value of X

Answer 1

The figure gives a dimension for the hypotenuse of 19

the height is given as 17, using the Pythagorean theorem we can find the base of the triangle:

19^2 = 17^2 + base^2

Simplify:

361 = 289 + base^2

Subtract 289 from both sides:

72 = base^2

Take the square root of both sides:

Base = 8.49 Round to 8.5

There are two identical triangles on each sides, so 8.5 x 2 = 17

The length of the two triangle bases is 17

The total base of the object is 31, so the length of the rectangular part in the middle would be 31 - 17 = 14

And X would be the same length as the bottom rectangle.

Therefore x = 14

Answer 2

x = 14

Explanation:

Inside the trapezoid, there are two right triangles, with a hypotenuse of 19 and a leg of 17. The other leg can be computed with the help of the pythagorean theorem as follows:

`{c}^(2) = {a}^(2) + {b}^(2) \\ {19}^(2) = {17}^(2) + {b}^(2) \\ 361 = 289 + {b}^(2) \\ 361 - 289 = {b}^(2) \\ 72 = {b}^(2) \\ √(72) = {b}^(2) \\ 8.5 = b`

Now, we can calculate the value of x, as follow;

8.5 + x + 8.5 = 31

17 + x = 31

x = 31 - 17

x = 14