A Side with an Expression

Part of the Triangles section of Coddy's Geometry journey. Lesson 59 of 71.

A matching side may be given as an expression instead of a number. In the figure, the small triangle has sides 4 and 6, and the large triangle has the matching sides x + 1 and 9.

$Two similar triangles: the small one has sides 4 and 6, the large one has the matching sides x plus 1 and 9$

A side labelled x + 1

Put the whole expression in the proportion, in brackets. Multiply both sides by 4, then subtract 1 from both sides:

(x + 1)/4 = 9/6

x + 1 = 6

x = 5

The proportion is written in the same way as before. The whole expression x + 1 stands in for the side. Multiplying both sides by 4 clears the fraction and leaves a short equation. A question may ask for the side itself rather than for x. Then substitute x = 5 into the expression. The side is x + 1 = 5 + 1 = 6.