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∆ABC ~ DEF. If area of ∆ABC = 9 sq. cm., area of ∆DEF =16 sq. cm and BC = 2.1 cm., find the length of EF.

Answer:

**Solution:-**

The square of any ratio between any two corresponding sides of two similar triangles is equal to the ratio of their areas.

From the question it is given that,

∆ABC ~ DEF

Area of ∆ABC = 9 sq. cm

Area of ∆DEF =16 sq. cm

We know that,

area of ∆ABC/area of ∆DEF = BC^{2}/EF^{2}

area of ∆ABC/area of ∆DEF = BC^{2}/EF^{2}

9/16 = BC^{2}/EF^{2}

9/16 = (2.1)^{2}/x^{2}

2.1/x = √9/√16

2.1/x = ¾

By cross multiplication we get,

2.1 × 4 = 3 × x

8.4 = 3x

x = 8.4/3

x = 2.8

**Therefore, EF = 2.8 cm**

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