Question

Line segment XY // BC of triangle ABC. Given AX: XB = 3:5, then the ratio
areas of trapezium XBCY and triangle AXY is​

Answer 1

Answer :-

1) in ∆AXY & ∆ABC

As XY // BC, corresponding angles are equal

ANGLE AXY = ANGLE ABC

ANGLE AYX = ANGLE ACB

∆ AXY ~ ∆ ABC

=> AX/AB = XY/BC

=> 3/8 = 18/BC

=> BC = 48 CM

2) AREA OF ∆AXY/ AREA OF ∆ABC = AX²/ AB² = 9/64

AREA OF ∆ ABC - AREA OF ∆AXY / AREA OF ∆ABC = 64-9/64

AREA OF TRAPEZIUM × BCY / AREA OF ∆ABC = 55/64

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Answer 2

AX

AB

XB

() In AAXY and AABC,

As XY BC, Corresponding angles are

equal

ZAXY = ZABC

LAYX = LACB

AAXY AABC

XY

AX

R BC

18

BC

BC = 48cm

(i)

Area of AAXY-AX

9

64

AB?

Area of A ABC

Area of AABC -Area of AAXY-64-9 55

64

Area of A ABC