Question

points C,D and E are not collinear. CD=10,CE=4, and DE=X. what are 3 possible lengths x can be so that CDE makes a triangle

Answer 1

x could be 9.2, 10 or 10.8.

Step-by-step explanation:

If the triangle to be formed would be an isosceles, then:

DE = x = 10.

If the triangle is a right angled with CD = 10 as the hypotenuse. Applying Pythagoras theorem, we have:

`10^(2)` =
`x^(2)` +
`4^(2)`

100 =
`x^(2)` + 16

100 - 16 =
`x^(2)`

`x^(2)` = 84

x =
`√(84)`

= 9.1652

≅ 9.2

If the triangle is a right angled with DE = x as the hypotenuse, then:

`x^(2)` =
`10^(2)` +
`4^(2)`

= 100 + 16

= 116

x =
`√(116)`

= 10.7703

x = 10.8