Area Problems
The lengths of three line segments (in cm) are given in each of the four cases. Which one of the following cases is not suitable to be the three sides of a triangle?
We know that in any triangle "the sum of two sides is always greater than its third side" and "the difference of two sides is always less than its third side".(i) 2 + 3 is not greater than 5 (ii) |5 - 2| not less than 3
Let the parallel sides be 3a and 5a.So Area of trapezium = 1/2 x sum of parallel side x perpendicular distance between them.? 1/2 (3a +5a) x 12 = 384? 8a = 64? a =8? Smaller side = 3x = 3 x 8 = 24 cm.
Let h be the altitude of triangle.So area of triangle = (1/2)xh area of square = x2From question area of square = area of triangle x2 = (1/2)xh ? h = (2x2)/x = 2x
In a triangleSum of two sides is always greater than 3rd side i.e., x < 25 + 15 = 40 .....(i)Difference of two sides is always less than 3rd side i.e., 25 - 15 = 10 < x ...(ii) From Eqs. (i) and (ii) , we get 10 < x < 40
EXAMIANS