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△ ABC and △ DEF are similar. The length of the smallest side of △ ABC is 2 units and the length of the smallest side of △ DEF is 5 units. The area of △ ABC is 4 units squared. What is the area, in units squared, of △ DEF ?
a. 8
b. 10
c. 15
d. 18
e. 25

Respuesta :

Answer:

e

Step-by-step explanation:

Given similar triangles with sides in the ratio a : b , then

ratio of areas = a² : b²

the ratio of corresponding sides = 2 : 5 , then

ratio of areas = 2² : 5² = 4 : 25

Let x be the area of Δ DEF , then by proportion [tex]\frac{ratio}{area}[/tex]

[tex]\frac{4}{4}[/tex] = [tex]\frac{25}{x}[/tex] ( cross- multiply )

4x = 4 × 25 = 100 ( divide both sides by 4 )

x = 25

The area of Δ DEF = 25 units²

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