Question

In triangle ABC, XY is parallel to BC. If area of triangle AXY is equal to area of the trapezium BCYX . Find AX:BX

Answer 1

Given : In triangle ABC, XY is parallel to BC  . area of triangle AXY is equal to area of the trapezium BCYX

To find : AX:BX

Solution:

area of ΔAXY =  area of the trapezium BCYX

area of ΔABC = area of ΔAXY + area of the trapezium BCYX

=> area of ΔABC = area of ΔAXY + area of ΔAXY

=>  area of ΔABC =  2 area of ΔAXY

=>  area of ΔABC / area of ΔAXY  = 2

as XY ║ BC

Hence ΔABC ≈  ΔAXY

Ratio of area of similar triangle  = ( ratio of corresponding sides)²

=> area of ΔABC / area of ΔAXY = (AX/AB)²

=>  2  = (AB/X)²

=> √2  = AB/AX

=> √2AX = AB

AB = AX + BX

=> √2AX = AX + BX

=> AX ( √2 - 1) = BX

=> AX/ BX = 1/ ( √2 - 1)

=> AX/ BX = √2+ 1

AX:BX  = √2+ 1

Learn more:

Ratio of area of 2 similar triangles are 2:3. Area of the larger triangle is

https://brainly.in/question/7877543

perimeters of two similar triangles are 30cm and 40cm respectively ...

https://brainly.in/question/18128501