Question

ABC is an isosceles triangle with base BC = 12cm. There is a rectangle GHED inside the triangle whose base GH is on side BC. HE =6, F is the mid point of BC. If AF =24, find the area of triangle

Answer 1

Answer:

Step-by-step explanation:

 As   AF = altitude,  CF = FB, The triangle ABC is isosceles.

 Then rectangle DEHG is symmetrically positioned around altitude.

  ΔAFC and EHC are similar.

      AF / FC = EH / HC   

      24 / 6 = 6 / HC

      HC = 1.50 cm

      So  FH = 6 - 1.50 = 4.50 cm

         GH = 9 cm

Area GHED = 9 * 6 = 54 cm²

  As EH is symmetrically positioned around AF (altitude) EF = HF = 3 cm.

     HC = 3 cm

 ΔGHC and ΔAFC are similar.

     GH / HC = AF / FC 

      GH = 3 * 24 / 6 = 12 cm

 

Area of rectangle = GHED =  6 * 12 = 72 cm²

MARK IT THE BRIANLIEST