Question

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

Answer 1

`CF=(35)/(2)`.

Explanation:

The area of the square is=81 square units

⇒
`(side)^(2)=81`

⇒
`side=9cm`

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

Now, Area of triangle EBF=
`(1)/(2){*}base{*}height`

53=
`(1)/(2){*}4{*}BF`

`BF=(53)/(2)`

As, BF=BC+CF

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

Therefore,
`(53)/(2)=9+CF`

`CF=(35)/(2)`.