Question

I need to solve this using the Pythagorean theorem to find the diameter of these 2 objects, weong answers will be deleted

Answer 1

○=> Solution (1) :

Given :

▪︎Length of a the hypotenuse of the triangle formed = 17 ft

▪︎Length of one of its leg = 15 ft

Let the length of another side or the diameter of the object be x.

We know that :

`\color{hotpink}\tt{hypotenuse}^(2) \color{plum}= {base}^(2) + {height}^(2)`

Which means :

`=\tt {x}^(2) + {15}^(2) = {17}^(2)`

`= \tt {x}^(2) = {17}^(2) - {15}^(2)`

`=\tt {x}^(2) = 289 - 225`

`= \tt {x}^(2) = 64`

`=\tt x = √(64)`

`\hookrightarrow\color{plum}\tt x = 8 \: ft`

▪︎Therefore, the diameter of this object = 8 ft

○=> Solution (2) :

Given :

▪︎Length of one of the legs of this triangle = 34 cm

▪︎Length of another leg of this triangle = 16 cm

Let the length of the hypotenuse of the triangle formed be x.

We know that :

`\color{hotpink}\tt{hypotenuse}^(2) \color{plum}= {base}^(2) + {height}^(2)`

Which means :

`= \tt {34}^(2) + {16}^(2) = {x}^(2)`

`= \tt\tt1156 + 256 = {x}^(2)`

`= \tt1412 = {x}^(2)`

`=\tt √(1412) = x`

`\hookrightarrow\color{plum}\tt 37 \: ft = x`

▪︎Therefore, the diameter of this object = 37 ft