A rectangular prism is 3 ft long 4 ft wide and 2 ft tall. What is the length of the longest diagonal?

Pythagorean Theorem in 3 D

sqrt ( 3^2 + 4^2 + 2^2) =

sqrt ( 9 + 16 + 4) =

sqrt( 29) = 5.3852 approximately

Step-by-step explanation:

The longest diagonal is about 8.9 inches. The longest length is going to be between the two longest lengths, the width and the height. The Pythagorean theorem is a^2 + b^2 = c^2. Plug the width and height into a and b of the Pythagorean equation. (4)^2 + (8)^2 = c^2. Now simplify the equation. 16 + 64 = c^2. 80 = c^2. Now find the square root of each side. (sqrt)80 = (sqrt)c^2. If you simplify this, you will find that c is equal to about 8.9 inches.

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: