Finding a Side

Part of the Triangles section of Coddy's Geometry journey. Lesson 53 of 71.

A proportion is an equation that says two ratios are equal. In similar triangles, the ratio of a large side to its matching small side is the same for every pair of matching sides. So two pairs of matching sides give a proportion. In the figure, the small triangle has sides 6 and 9, and the large triangle has the matching sides x and 15.

$Two similar triangles: the small one has sides 6 and 9, the large one has the matching sides x and 15$

Sides 6 and 9 match x and 15

Write each fraction as a large side over its matching small side, then solve:

x/6 = 15/9

x = 10

To solve the proportion, multiply both sides by 6: x = 90/9 = 10.

You can write the proportion in more than one way. You can put the large side over the small side in both fractions, or the small side over the large side in both. Each fraction must pair a side with its matching side. You can also put the two sides of the large triangle in one fraction and the two sides of the small triangle in the other. The proportion x/15 = 6/9 is written this way, and it gives the same answer, x = 10. Never write a fraction that pairs a side with a side it does not match.