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coplanar squares abgh and bcdf are adjacent, with cd=10 units and ah=5 units. point e is on segments ad and gb what is the area of triangle abe, in square units? express your answer in a common fraction.

coplanar squares abgh and bcdf are adjacent, with cd=10 units and ah=5 units. point-example-1

1 Answer

1 vote

Answer-


\boxed{\boxed{\text{Area}_(ABE)=(25)/(3)\ unit^2}}

Solution-

ΔABE ~ ΔACD by AA (Angle-Angle) similarity, as

  1. m∠BAE = m∠CAD (as ∠A is common to both)
  2. m∠ABE = m∠ACD = 90° (As each angles of a square is 90°)

According to the similarity of triangles,


\Rightarrow (AB^2)/(AC^2)=\frac{\text{Area}_(ABE)}{\text{Area}_(ACD)}


\Rightarrow (AB^2)/((AC)^2)=\frac{\text{Area}_(ABE)}{(1)/(2)* AC* CD}


\Rightarrow (AB^2)/((AB+BC)^2)=\frac{\text{Area}_(ABE)}{(1)/(2)* (AB+BC)* CD}


\Rightarrow (5^2)/((5+10)^2)=\frac{\text{Area}_(ABE)}{(1)/(2)* (5+10)* 10}


\Rightarrow (5^2)/(15^2)=\frac{\text{Area}_(ABE)}{(1)/(2)* 15* 10}


\Rightarrow (25)/(225)=\frac{\text{Area}_(ABE)}{75}


\Rightarrow \text{Area}_(ABE)=(25* 75)/(225)


\Rightarrow \text{Area}_(ABE)=(25)/(3)\ unit^2

User Mark Biek
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