Find the diagonal mn of the prism mezafun

MN = sqrt(34)

Step-by-step explanation:

First, draw the segment FN. The diagonal, MN, of the prism is the hypotenuse of triangle NFM. Triangle NFM is a right triangle with legs FN and FM and hypotenuse MN.

Leg FM of triangle NFM has length 4 cm.

We need to find the length of leg FN.

Look at the base of the prism which is square UNAF. FN is a diagonal of that square. Now think of right triangle FUN with legs UN and UF, each of length 3 cm. We can find FN with the Pythagorean theorem.

(UF)^2 + (UN)^2 = (FN)^2

3^2 + 3^2 = (FN)^2

(FN)^2 = 18

FN = sqrt(18)

Now we know FN. We use FN and FM as legs and find MN, the hypotenuse of triangle NFM.

(FN)^2 + (FM)^2 = (MN)^2

18 + 4^2 = (MN)^2

18 + 16 = (MN)^2

(MN)^2 = 34

MN = sqrt(34)

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step-by-step explanation:

x=6 and x=3

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