KnowledgeBoat Logo

Mathematics

△ABC ~ △DEF. If BC = 3 cm, EF = 4 cm and area of △ABC = 54 sq.cm, determine the area of △DEF.

Similarity

26 Likes

Answer

Let the area of △DEF be x sq.cm

We know that, the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.

∴Area of △ABCArea of △DEF=BC2EF2⇒54x=3242⇒54x=916⇒x=54×169⇒x=6×16⇒x=96.\therefore \dfrac{\text{Area of △ABC}}{\text{Area of △DEF}} = \dfrac{BC^2}{EF^2} \\[1em] \Rightarrow \dfrac{54}{x} = \dfrac{3^2}{4^2} \\[1em] \Rightarrow \dfrac{54}{x} = \dfrac{9}{16} \\[1em] \Rightarrow x = \dfrac{54 \times 16}{9} \\[1em] \Rightarrow x = 6 \times 16 \\[1em] \Rightarrow x = 96.

Hence, the area of △DEF = 96 sq.cm.

Answered By

16 Likes

Related Questions