Question

Through a point on the hypotenuse of a right triangle, lines are drawn parallel to the legs of the triangle so that the triangle is divided into a square and two smaller right triangles. The area of one of the two small right triangles is m times the area of the square. The ratio of the area of the other small right triangle to the area of the square is:___________.
(A) 1/(2m + 1)
(B) m
(C) 1 - m
(D) 1/(4m)
(E) 1/(8m^2)

Answer 1

Answer: D 1/4m

Step-by-step explanation:

Similarly in Mathematics shows that two right triangles are similar. Thus the ratio of the sides of the triangles are the same. Since A = 1/2bh = h/2, according to the figure, the height of the triangle with area m is 2m. Therefore 2m/1 = 1/x  where x is the base of the other triangle. X = 1/ 2m,

The ratio of the area of the other small right triangle to the area of the square is the area of that triangle which is

 1/2 × 1 × 1/2m = 1/4m

please find the attached file for the figure.