Q:

Here is a test to how good your math is,In ∆ABC , A = ( 1 , 2 ) ; B = ( 5 , 5 ) and <ACB = 90° . If area of ∆ABC is to be 6.5 square units , then the possible number of points for C is ?

Accepted Solution

A:
Answer:ZeroStep-by-step explanation:The distance AB is ...... √((5-1)²+(5-2)²) = √(16+9) = 5The largest right triangle that can be constructed with AB as the hypotenuse is one with an altitude of 5/2 = 2.5 units. Its area will be ...... (1/2)·5·2.5 = 6.25 . . . . square unitsIt is not possible to construct the triangle ABC described. _____In order to achieve the given area, ∠C would need to be 87.75° or smaller. It could not be 90°.