Question

How does the area of triangle RST compare to the area of triangle LMN? The area of △RST is 2 square units less than the area of △LMN. The area of △RST is equal to the area of △LMN. The area of △RST is 2 square units greater than the area of △LMN. The area of △RST is 4 square units greater than the area of △LMN.

Answer 1

The answer would be B

Answer 2

Inscribe triangle RST in the square with dimensions 4×4, as shown in the figure.

from the area of this square, 4*4=16, we remove the triangles with dimensions
3×4, 2×1 and 2×4, whose side lengths are shown in the figure, and we are left with the area of triangle RST.


so
`Area(RTS)=16- (1)/(2)*3*4- (1)/(2)*2*1- (1)/(2)*2*4=16-6-1-4=5` units squared

similarly,


`Area(LMN)=4*3- (1)/(2)*1*4- (1)/(2)*2*2- (1)/(2)*2*3=12-2-2-3=5` units squared

Thus, the areas are equal.