XY is drawn parallel to BC in triangle ABC, with X on AB and Y on AC, and AX : AB = 3 : 5. The area of trapezium XBCY exceeds the area of triangle AXY by 42 cm^2. Find the area of triangle AXY (in cm^2).

Question

Accepted Answer

54. area(AXY) : area(ABC) = (3/5 )^2 = 9/25. Write area(AXY) = 9k and area(ABC) = 25k, so trapezium XBCY = 16k. Then 16k - 9k = 7k = 42, giving k = 6 and area(AXY) = 9 × 6 = 54 cm^2. The option 96 is the trapezium and 150 the whole triangle; 21 is simply half of the 42 cm^2 difference.

XY is drawn parallel to BC in triangle ABC, with X on AB and Y on AC, and AX : AB = 3 : 5. The area of trapezium XBCY exceeds the area of triangle AXY by $42 cm^{2}$ .
Find the area of triangle AXY (in $cm^{2}$ ).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Areas of Similar Triangles practice

XY is drawn parallel to BC in triangle ABC, with X on AB and Y on AC, and AX : AB = 3 : 5. The area of trapezium XBCY exceeds the area of triangle AXY by 42cm2.Find the area of triangle AXY (in cm2).

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Areas of Similar Triangles practice

XY is drawn parallel to BC in triangle ABC, with X on AB and Y on AC, and AX : AB = 3 : 5. The area of trapezium XBCY exceeds the area of triangle AXY by $42 cm^{2}$ .
Find the area of triangle AXY (in $cm^{2}$ ).