kyliemckenna55 kyliemckenna55
  • 14-01-2019
  • Mathematics
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The area of square ABCD is 81 square units and the area of triangle EBF is 53 square units. If EB is perpendicular to BF and AE=5, find the length of CF

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boffeemadrid
boffeemadrid boffeemadrid
  • 23-01-2019

Answer:

[tex]CF=\frac{35}{2}[/tex].

Step-by-step explanation:

The area of the square is=81 square units

⇒[tex](side)^{2}=81[/tex]

⇒[tex]side=9cm[/tex]

From figure, AB= 9cm, and it is given that AE=5cm, therefore EB=4cm.

Now, Area of triangle EBF=[tex]\frac{1}{2}{\times}base{\times}height[/tex]

53=[tex]\frac{1}{2}{\times}4{\times}BF[/tex]

[tex]BF=\frac{53}{2}[/tex]

As, BF=BC+CF

And BC is the sie of square which is equal to 9cm

Therefore, [tex]\frac{53}{2}=9+CF[/tex]

[tex]CF=\frac{35}{2}[/tex].

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