Solve the proportion for x.
1 answer:
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Step-by-step explanation:
Here is the solution...hope it helps:)
Answer:
The length of the diagonal of the cube = √(3 × 10²) = √300 cm
Step-by-step explanation:
* Lets revise the properties of the cube
- It has six equal faces all of them are squares
- It has 12 vertices
- The diagonal of the cube is the line joining two vertices in opposite
faces (look to the attached figure)
- To find the length of the diagonal do that:
# Find the diagonal of the base using Pythagoras theorem
∵ The length of the side of the cube is L
∵ The base is a square
∴ The length of the diagonal d = √(L² + L²) = √(2L²)
- Now use the diagonal of the base and a side of a side face to find the
diagonal of the cube by Pythagoras theorem
∵ d = √(2L²)
∵ The length of the side of the square = L
∴ The length of the diagonal of the cube = √[d² + L²]
∵ d² = [√(2L²)]² = 2L² ⇒ power 2 canceled the square root
∴ The length of the diagonal of the cube = √[2L² + L²] = √(3L²)
* Now lets solve the problem
∵ The length of the side of the square = 10 cm
∴ The length of the diagonal of the cube = √(3 × 10²) = √300 cm
- Note: you can find the length of the diagonal of any cube using
this rule Diagonal = √(3L²)
<em>Answer:</em>
<h2><em>x=</em><em>6</em><em>√</em><em>2</em></h2><em>please </em><em>see</em><em> the</em><em> attached</em><em> picture</em><em> for</em><em> full</em><em> solution</em><em>.</em><em>.</em><em>.</em>
<em>Hope </em><em>it</em><em> helps</em><em>.</em><em>.</em><em>.</em>
<em>Good </em><em>luck</em><em> on</em><em> your</em><em> assignment</em><em>.</em><em>.</em><em>.</em><em>.</em>
