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# Similar shapes

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qualitystreet  May 16, 2018
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Hi QS!

Since the two shapes are similar, we can set up the following relationship:

Assumption 1: triangle ABE is similar to ACE, CD and BE is parallel

$$\frac{15}{15+3}=\frac{10}{10+x}\\ 15(10+x)=10\cdot{18}\\ 150+15x=180\\ 15x=30\\ x=2$$

Assumption 2: triangle ABE is similar to ACE, CD and BE are not paralle

$$\frac{10}{15+3}=\frac{15}{10+x}\\ 10(10+x)=15\cdot18\\ 100+10x=270\\ 10x=170\\ x=17$$

I hope this helped,

Gavin

GYanggg  May 16, 2018
edited by GYanggg  May 16, 2018