How are algebraic properties applied in the steps to solving equations?
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What you have here is a situation with two <em>similar triangles. </em>The triangle in the lower left is similar to the triangle in the upper right - I've included an image with "cutouts" of those triangles so you can see the similarities. Similar triangles have a very important property: <em>the ratios of their corresponding sides are equivalent</em>. Here, we can set up a ratio between the sides of length 64 and x on the larger triangle, and the corresponding sides of length x and 36 on the smaller triangle. Setting the two equal to each other, we have
Multiplying both sides of the equation by 36 and x, we get
finally, we take the square root of both sides of the equation to find x:
Multiplying both sides of the equation by 36 and x, we get
finally, we take the square root of both sides of the equation to find x: