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Vlad1618 [11]
2 years ago
6

Homework 1:Pythagorean Theorem and it’s Converse Find The Value of X

Mathematics
2 answers:
Viefleur [7K]2 years ago
3 0

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

kvasek [131]2 years ago
3 0

Answer:

x = 14

Step-by-step 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}  \\  \sqrt{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

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