How to Calculate Similar Triangles

Similar triangles are triangles of different physical size, but the ratios or the relationship between the sides are the same on both triangles. Because the ratios are the same, you can use the ratios to calculate the lengths of the sides of one triangle based on the length of a similar triangle. You need the length of all sides of one triangle and the length of just one side of the other triangle.

Instructions

    • 1

      Find the length of all three sides of one triangle. As an example, assume the sides of triangle A have the following lengths: side "a" is 4 inches, side "b" 6 inches and side "c" is 8 inches.

    • 2

      Find the length of one side of a similar triangle. As an example, assume you have only side "a" of triangle B which is a similar triangle to triangle A. Assume side "a" of triangle B is 6 inches. Note, side "a" in triangle A and side "a" in triangle B are referred to as corresponding sides.

    • 3

      Find the ratio using the known corresponding sides according to the following formula: ratio = (known corresponding side of first triangle)/(known corresponding side of second triangle). Using the example, ratio = side a of triangle A/side a of triangle B. In the example, the ratio is 4/6, or 2/3.

    • 4

      Calculate the unknown sides using the ratio. Side b of Triangle B = (Side b of triangle A) x (ratio). Using the example, (6) x (2/3) = 4 inches. Side c of Triangle B = (Side c of triangle A) x (ratio). Using the example, (8) x (2/3) = 5.33 inches.

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