Question

in triangle abc , angle b = 90 degree , BE is the perpendicular bisector of the AC ,then ar(triangle DEF)/ar(triangle ABC).​

Answer 1

Answer:

Firstly, we can state that,

(1)  Area of AYXArea of ABC=518  

This is because it is given that,

Area of BXYCArea of ABC=1318  

and,

Area of ABC=Area of AYX+Area of BXYC .

Next we can state that,

(2)  AB24×AC2=518  

This is because  ABC  and  AYX  are similar triangles. So the ratio of their areas is the same as the square of ratio of the lengths of their sides. This gives us

AX2AC2=518 .

Add to this the fact that  AX=AB2  is a given condition.

Next we can state that,

(3)  AC2+1224×AC2=518  

This is because,

AB2=AC2+122  

using Pythagoras theorem, and since we know that  BC=12 .

This can now be solved for  AC .