If the cube shown is 5 inches on all sides, what is the length of the diagonal, x, of the cube?
2.75 inches
35 inches
5
inches
5.75 inches

To do this, we need to find the length of the diagonal of the face, in this diagram, from A to B and then we can construct a triangle with AB and BC as the two legs, and CA as the hypotenuse.

We can find the diagonal by using the Pythagoras Theorem.

First, we need to find the length of AB.

a2+b2=c2

s2+s2=d2

s22=d2

s=5

522=d2

We can now use algebra to find out the length of the diagonal of the square, which is the shorter diagonal of the cube.

522=d2

25×2=AB2

50=AB2

AB2=50

AB=√50

√50

√50=√2×√52

√50=√2×5

√50=5√2

AB=5√2

Now we can construct the triangle and find the overall longer diagonal of the cube.

a2+b2=c2

AB2+BC2=CA2

AB=5√2

BC=5 because BC is simply an edge of the cube.

(5√2)2+52=CA2

Now we can use algebra to find CA

√502+52=CA2

The square root and square of 50 cancel each other out.

50+52=CA2

50+25=CA2

75=CA2

√75=√CA2

√75=CA

√75≈8.660

75=3×52

√75=√3×√52

√75=√3×5

√75=5√3

CA=√75

CA=5√3

CA≈8.660

And if you wanted to do it the other way, the formula is:

d=√3×a

d=√3×5

d=5√3

Step-by-step explanation:

To find the diagonal of the cube, there are 2 methods, using a formula or by using the Pythagorus Theorem. So that this explanation is more interesting - and so that you're not just putting numbers into a formula - I am going to tell you how to do the Pythagorus theorem way.

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step-by-step explanation: