I'm reviewing my most hated math: Geometry. I do not know how to get the answer to this question.
Triangle ABC is to be drawn so that the length of side AC is greater than 3 and less than 5. If the length of the perpendicular drawn from point B to side AC is less than 8, which of the following CANNOT be the area of the triangle.
(A) 8
(B) 10
(C) 16
(D) 18
(E) 36
Hi Mariolee,
you can stand the triangle on "any" of it's 3 sides.
The area of the triangle is the same no matter which side we stand it on.
suppose we stand it on side AC.
Then point B will be the topmost point and is less than 8 units above AC.
So the perpendicular height is less than 8.
The base AC is between 3 and 5 units long.
A triangle is half of a parallelogram.
a parallelogram has the same area as a rectangle of same base and perpendicular height.
The rectangle's area is (base)(height).
the triangle's area is half that.
We don't know the height of the triangle, only that it cannot be 8 or more.
Hence the triangle's area cannot reach 0.5(5)8 square units.