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AdorableApatosaurus7671

Hello, I need help with this question!!! Thank you so much ;))))

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Louis-Philippe B

Thank you for your question!

First, it is important to remember that this is the two-dimensional projection of a three-dimensional rectangular prism. Considering this, we can establish that :

$$ m\overline{CD} = 14 $$

Knowing this, and knowing that rectangles ABCF and CDEF are similar, we can tell that :

$$ \frac{m\overline{AF}}{m\overline{FC}} = \frac{m\overline{FC}}{m\overline{CD}} $$

Replacing these measures for actual values, we find that :

$$ \frac{56}{x} = \frac{x}{14} $$

Using a cross-product, we find that :

$$ 56•14 = x^2 $$

$$ x = 28\:cm $$

Don't hesitate if you need more help!

FerUpsilon5520

Since the prism has a surface equal to that of a cube of side c:

2(56x) + 2(14x) + 2(56·14) = 6c² (1)

and

since ABCF and CDEF are similar

mAF/MFC = mEF/mFE

56/x = x/14

=> x² = 56·14 = ....

replacing x by its value in (1) will give you the value of c

Note: the sentence " In addition mCD < mCF < mAF" was not useful as it was specified that the figure is a right rectangular prism.