Area Problems
A rectangle has 15 cm as its length and 150 cm 2 as its area .Its area is increased to 1 1 / 3 times the original area by increasing only its length . Its new perimeter is?
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
Area of equilateral triangle = ?3a2/4 = x ......(i)And perimeter = 3a = y ? a = y/3 ....(ii)Now, Putting the value of a from Eq. (ii) in Eq. (i). we get?3 (y/3)2/4 = x ? x = ?3 x y2/36? x = y2/3?3x = y2/12?312?3 x = y2On squaring both sides, we get y4 = 432x2
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.
EXAMIANS