ABC ~ ∆DEF. If AB = 4 cm, BC = 3.5 cm, CA = 2.5 cm andDF = 7.5 cm, the perimeter of∆DEF is
Question
ABC ~ ∆DEF. If AB = 4 cm, BC = 3.5 cm, CA = 2.5 cm andDF = 7.5 cm, the perimeter of∆DEF is
Solution
Given that triangle ABC is similar to triangle DEF, the sides are proportional.
The ratio of the sides AB and DF is 4/7.5 = 0.5333.
Since the triangles are similar, this ratio will be the same for the corresponding sides BC and EF, and CA and DE.
So, to find the lengths of EF and DE, we multiply the lengths of BC and CA by the ratio:
EF = BC * (DF/AB) = 3.5 * (7.5/4) = 6.5625 cm DE = CA * (DF/AB) = 2.5 * (7.5/4) = 4.6875 cm
The perimeter of a triangle is the sum of the lengths of its sides, so the perimeter of triangle DEF is:
P = DF + EF + DE = 7.5 cm + 6.5625 cm + 4.6875 cm = 18.75 cm
So, the perimeter of triangle DEF is 18.75 cm.
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