The Unknown Below

Part of the Triangles section of Coddy's Geometry journey. Lesson 54 of 71.

Sometimes the unknown is in the denominator of a fraction. In the figure, the small triangle has sides 3 and 5, and the large triangle has the matching sides 6 and x.

$Two similar triangles: the small one has sides 3 and 5, the large one has the matching sides 6 and x$

Sides 3 and 5 match 6 and x

Write the proportion. Multiply both sides by 5 and by x to clear the denominators, then divide both sides by 3:

3/5 = 6/x

3x = 30

x = 10

Multiplying both sides by x and by 5 clears the denominators and turns the proportion into an ordinary equation. This step is called cross-multiplying. Each numerator is multiplied by the denominator on the other side of the equals sign. Another way is to flip both fractions first, which gives 5/3 = x/6. Now x is on top, and you only need to multiply both sides by 6. Flipping is allowed because the two fractions are equal, and flipping both of them keeps them equal.