Question

Let A be the area of a triangle with sides of length 25, 25, and 30. Let B be the area of a triangle with sides of length 25, 25, and 40. What is the relationship between A and B? (A) A= 9 16 B (B) A= 3 4 B (C) A=B (D) A= 4 3 B (E) A= 16 9 B

Answer 1

(C) A = B

Explanation:

The altitude of ΔA divides it into two right triangles with hypotenuse 25 and leg 15. The other leg will be √(25² -15²) = 20, so the area is ...

A = (1/2)(20)(30) = 300 . . . square units

The altitude of ΔB divides it into two right triangles with hypotenuse 25 and leg 20. The dimensions of this right triangle match those of the right triangles that makeup ΔA. The altitude has length 15, so the area is ...

A = (1/2)(40)(15) = 300 . . . square units

The areas of the two triangles are equal.