Problem Solving

abhirup1711 wrote:If two sides of a triangle are 12 and 8 in length, which of the following could be the area of the triangle?
l.35
2. 48
3. 56

A) 1 only
B) 1 and 2 only
C) 1 and 3 only
D) 2 and 3 only
E) 1, 2 and 3

Please help

First, we can take the two given sides and make the angle between them as small as we want. As we make that angle smaller and smaller, the area of the triangle will approach zero.

The area of a triangle = (1/2)(base)(height)
Let's make one side the base. Let's say the side with length 12 is the base.
In order to maximize the area of the triangle, we need to maximize its height. This will occur when the two given sides meet at a 90-degree angle. So, the maximum height is 8, which means the maximum area = (1/2)(12)(8) = 48

So . . . 0 < area < 48, which means the area could be 35 and 48 (but not 56).

Answer = B

Cheers,
Brent