Question

Please ΔEFU ~ ΔVWU. Find the length of UF.

Answer 1

Answer: UF = 11

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Explanation:

In EFU, we see that EU are the first and last letters. In VWU, we see that VU are the first and last letters. This order is important to be able to pair EU with VU

So EU/VU is one ratio

The other ratio is UF and UW, which are the last two letters of EFU and VWU respectively. So the other ratio is UF/UW

Set the ratios equal to each other and solve for x

EU/VU = UF/UW

7/35 = x/55

7*55 = 35*x ... cross multiply

385 = 35x

35x = 385

x = 385/35 .... divide both sides by 35

x = 11

UF = 11

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Or you could note how UV = 35 is exactly 5 times larger compared to EU = 7

That must mean WU = 55 must also be 5 times larger compared to UF = x

So,

WU = 5*UF

55 = 5x

5x = 55

x = 55/5

x = 11

UF = 11

This is similar to the previous section because UV/EU = 35/7 = 5 is the scale factor.