# In the Following Figure, Seg Dh ⊥ Seg Ef and Seg Gk ⊥ Seg Ef. If Dh = 18 Cm, Gk = 30 Cm and A(Triangle Def) = 450 Cm^2, Then Find - Geometry

In the following figure, seg DH ⊥ seg EF and seg GK ⊥ seg EF. If DH = 18 cm, GK = 30 cm and A(triangle DEF) = 450 cm^2, then find:

1) EF

2) A(triangle GFE)

3) A(square DFGE)

#### Solution

1) Area of a triangle = 1/2 x base x height

:. A(triangle DEF) = 1/2 xx EF xx DH

:. 450 = 1/2 xx EF  xx 18 ......(Substituting the given values)

:. (450xx2)/18 = EF

:. EF = 50    :. EF = 50 cm

2) triangle DEF and triangle GEF have then  common base EF

∴ their areas are proportional to their corresponding heights

:. (A(triangle DEF))/(A(triangle GEF)) = "DH"/"GK"

:. 450/(A(triangle GEF))  = 18/30  ....(Substituting the given values).

:. A(triangle GEF) = (450xx30)/18 =  750 cm^2

:. A(triangle GEF) = 750 cm^2

3) A(squareDFGE) = A(squareDEF) + A(squareGEF) ....(Area addition postulate)

= 450 +  750 = 1200cm2

:. A(squareDFGE) = 1200 cm^2

Concept: Similarity of Triangles
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