Question

If ∆ABC ~ ∆DEF, BC = 3EF and ar (∆ABC) = 117cm² find area (∆DEF).

Answer 1

Two Triangles are said to be similar if their i)corresponding angles are equal and ii)corresponding sides are proportional.(the ratio between the lengths of corresponding sides are equal)

•Similarity of triangles should be expressed symbolically using correct correspondence of their vertices

SOLUTION:

GIVEN:
∆ABC ~  ∆DEF
ar(∆ABC) = 117 cm²
BC = 3EF

ar( ∆ABC) / ar( ∆DEF ) = (BC / EF)²
[The ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides]

117 / ar( ∆DEF ) = (3EF /EF)²
117 / ar( ∆DEF ) = (3 /1)²
117 / ar( ∆DEF ) = 9/1
9 ×  ar( ∆DEF )  = 117
ar( ∆DEF )  = 117/9
ar( ∆DEF )  = 13 cm²

Hence, the  ar( ∆DEF ) = 13 cm²

HOPE THIS WILL HELP YOU....

Answer 2

★ Here is your answer ★