Question

Cakes, yummy and fluffy always make our salivary glands tingle! If Goutham ate part 1 of the cake shown below and Pavani ate part 2 of the cake, who ate more cake? (Cake is nearly square in shape)

Answer 1

Since cake is square in shape, we can analyze it in form of a square.

In $\Delta CDPand\Delta CBP$

CD= CB (Sides of a square)

$\angle DCP$ = $\angle BCP$ = ${45}^o$

CP = CP (Common)

In $\Delta CDP\cong \Delta CBP$ (By SAS congruency condition)

Area ($\Delta CDP$ ) = Area ($\Delta CBP$)

$\Delta CDOand\Delta CBO$

CD= CB (Sides of a square)

$\angle DCO$ = $\angle BCO$ = ${45}^o$

CO = CO (Common)

$\Delta CDO\cong \Delta CBO$ (By SAS congruency condition)

Area ($\Delta CDO$) = Area ($\Delta CBO$)

From I and II we can say that,

Area 1 = Area 2

So Goutham and Pavani ate equal parts of cake.