Question no. 21(I)

Question no. 21(I) 17. The perimeter of a triangle is 8 cm. If one of the sides is 3 cm, what are the lengths the other sides for maximum area of the triangle? Hint. a + b + c —8 s = 4. Let a 3 cm, then b + c = 5 b = 5— c. If A is area of triangle, then A2 = s(s — a) (s — b) (s — c) A2 = 4 (c — 1) (4 — c). A will be maximum when A2 is maximum. 18. A sheet of paper is to contain 18 cm2 of printed matter. The margins at the top and bottom are 2 cm each, and at the sides 1 cm each. Find the dimensions of the sheet which require the least amount of paper. 19. Show that of all rectangles inscribed in a given fixed circle the square has the maximum area. 20. (i) The sum Of perimeters Of a circle and a square is k, where k is some constant. prove that the sum of their areas is least when the side of the square is double the radius of the circle. (NCERT) (ii) Given the sum of perimeters of a circle and a square, show that the sum of areas is least when the diameter of the circle is equal to the side of the square. 21. (i) A wire 10 metres long is cut into two parts. One part is bent into the shape of a circle and the other into the shape of an equilateral triangle. How should the wire be cut so that the combined area of the two figures is as small as possible? (ii) A wire of length 36 cm is cut into two pieces. One of the piece is turned into the form of a square and the Other in the form of an equilateral triangle. Find the length Of each piece so that the sum of the areas of the two figures be minimum. Hint. (ii) Let the length of the piece bent in the form of a square be x cm, then the lengf of the piece bent in the form of an equilateral triangle is (36 — x) cm. Let S be tl combined area of the two figures, then 2 x