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Rahul@gurome wrote:The triangle will have a maximum area when it is a right angled triangle. If we take 8 as the base and 5 as the height of right angled triangle, then area of triangle = (1/2) × 8 × 5 = 20.
This means that triangle can have a maximum area of 20 sq units, which means II and III are both true.
The correct answer is (D).
The biggest triangle possible will be formed if the known sides (8 and 5) are the base and height of a right triangle. To illustrate, imagine that the triangle lays flat on its side of 8. The largest triangle possible will be formed with the longest height available. This is achieved if the side of 5 stands vertically. If 5 isn't straight up but slanted, then the height will in fact be less than 5. Thus the greatest triangle has base=8 height=5, area=20.kartheekchoudhary wrote:One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?
I 24
II 20
III 5
D
There is no lower bound on the area of any triangle when you only know two sides (actually area > 0). This is because the area will be decided by the angle between the two known sides. Above I explained why a 90 degree angle creates the maximum area. As this angle gets smaller (60 degrees) and smaller (15 degrees), you can visualize the area shrinking until it approaches 0 when the angle approaches 0 degrees. So the area could be 5, 3, 1, or 0.0003.krazy800 wrote:could you please explain how option III or 5 could be true?
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