Is there a triangle that one side of length 4 inches , one side of length 2 inches and one side of length 1 in? explain

According to the Triangle inequality theorem, this does not work

For a triangle to be valid, the length of any two sides added together must by greater than the length than the third side.

In this example, we can see that the side with length 1 added to the side with length 2 is equal to 3inches.

3 inches is less that 4inches (the length of the 3rd side). So that triangle does not work.

Answer

This triangle does not work, because the sum of the lengths of any two sides of a triangle is  NOT  greater than the length of the third side.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.