Answer:
Therefore the Area of ΔEDF is 9.6 in².
Step-by-step explanation:
Given:
ΔBAC ~ ΔEDF
EF = 4 in
BC = 5 in
Area of ΔBAC = 15 in²
To Find:
Area of ΔEDF = ?
Solution:
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
This proves that the ratio of areas of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.
ΔBAC ~ ΔEDF ........Given
Therefore we will have
[tex]\dfrac{\textrm{Area of triangle BAC}}{\textrm{Area of triangle EDF}}=\dfrac{BC^{2}}{EF^{2}}= \dfrac{BA^{2}}{ED^{2}}=\dfrac{AC^{2}}{DF^{2}}[/tex]
Substituting the values we get
[tex]\dfrac{15}{\textrm{Area of triangle EDF}}=\dfrac{5^{2}}{4^{2}}=\dfrac{25}{16}\\\\\textrm{Area of triangle EDF}=\dfrac{240}{25}=9.6\ in^{2}[/tex]
Therefore the Area of ΔEDF is 9.6 in².
