Answer: AB is 14 units long.
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Explanation:
We're told that [tex]\triangle ABC \sim \triangle DE F[/tex] which means triangle ABC is similar to triangle DEF. The order of the letters is important as you'll see in the next two paragraphs.
AB and DE are the first two letters of ABC and DEF respectively. These two sides pair up as one corresponding pair. This forms the fraction AB/DE.
Through similar logic, we get the fraction BC/EF. We have BC and EF as the last two letters of ABC and DEF respectively. This fraction is equal to the previous fraction we set up (due to similar triangles having equal proportions).
Once again, the order of the letters matters to tell us how the sides and angles pair up together.
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In short, the key takeaway from that last section is that we can form this equation:
AB/DE = BC/EF
From here, we apply substitution and solve for x
So,
AB/DE = BC/EF
7x/7 = 4/x
7x*x = 7*4 .... cross multiplication
7x^2 = 28
x^2 = 28/7
x^2 = 4
x = sqrt(4)
x = 2
We only consider the positive square root because x is some side length. Negative x values are not allowed.
To wrap things up, use that x value to find AB
AB = 7x = 7*2 = 14
