Area Problems
The sides of a triangle area in the ratio of 1/3 : 1/4 : 1/5 and its perimeter is 94 cm. Find the length of the smallest side of the triangle .
Given ratio = 1/3 : 1/4 : 1/5 = 20 : 15 : 12Let length of the sides be 20k, 15k and 12k.Then, according to the question,20k + 15k + 12k = 94? 47k = 94? k = 94/47 = 2Smallest side = 12k = 12 x 2 = 24 cm
Area of the square field = 1 hectare = 10000 m2Side of the square = ? 10000 m = 100 mSide of another square field = 100 + 1 = 101 m? Required difference of area = [(101)2 - (100)2] m2=[(101 + 100 ) (101 - 100) ] m2= 201 m2
Let there be n sides of the polygon. Then it has n vertices. The total number of straight lines obtained by joining n vertices by talking 2 at a time is nC2 These nC2 lines also include n sides of polygon. Therefore, the number of diagonals formed is nC2 - n. Thus, nC2 - n = 44? [n(n - 1)/2] - n = 44? ( n2 - 3n) / 2 = 44? n2 - 3n = 88 ? n2 - 3n - 88 = 0 ?(n - 11) (n + 8) = 0 ? n = 11
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