The perimeters of two similar triangles are 30 cm and 20 cm respectively. If one side of the first triangle is 12 cm, determine the corresponding side of the second triangle

Step 1: Investigate the given question and write the given values
NOTE: The two triangles are similar
EXAMPLE: ∆ABC ~ ∆PQR
Perimeter of △ABC = 20 cm.
Perimeter of △PQR = 30 cm.
One side of the first triangle QR = 12 cm, BC = ?
Step 2: Utilize the similarity principle to solve this
NOTE: If two triangles are similar then ratio of the perimeters of the
triangles is equal to the ratio of their corresponding sides.
\frac{perimeter of ABC}{perimeter of PQR} = \frac{BC}{QR}
Step 3: Substitute the known values and simplify
EXAMPLE: \frac{20}{30} = \frac{BC}{12}
\frac{20 * 12}{30} = BC
BC = 8 cm
So required value of the corresponding side is 8 cm