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Question Paper Class IX

Mathematics

Set 3

Page 3

Ques 16. Draw a histogram and frequency polygon for the distribution of weights (in kg) for 65 persons.

Ans:

Weight (in kg)	Number of persons
50-55	12
55-60	8
60-65	15
65-70	6
70-75	5
75-80	10
80-85	5
85-90	4

Ques 17. Show that the sum of four angles of a quadrilateral is four right angles.

Ans:
Given ÷ A quadrilateral ABCD
To prove ÷ ÐA + ÐB + ÐC + ÐD = 360°

Construction ÷ Join BD

Proof ÷ we have - In D ABD
Ð1 + Ð2 + Ð6 = 180° -(1)
[sum of angles of a D = 180°]
In D BCD
Ð3 + Ð4 + Ð5 = 180° [Sum of angles of a D = 180°] -(2)
Adding (1) and (2)
Ð1 + Ð2 + Ð6 = Ð3 + Ð4 + Ð5 = 180 + 180
Þ (Ð1 + Ð4) + (Ð2 + Ð3) + Ð6 + Ð5 = 360°
Þ ÐD + ÐB + ÐA + ÐC = 360°
Hence proved

Ques 18. Divide 375 among A, B and C so that A may have Rs 40 more than B and C had Rs 35 more that A
Ans: Let share of B = x Rs Share of A = Rs (x+40) Share of C = Rs (x+35) By the condition x + x + 40 + x + 35 = 375 3x + 75 = 375 3x + 75 - 75 3x = 300 x = 300/3 = 100 \ share A = Rs.100 + 40 = Rs.140 Share of B = Rs.100 Share of C = 100 + 35 = Rs. 135

Ques 19. The perimeter of an isosceles triangle is 108 cm and its base is 48 cm find the area of the triangle
Ans: In D ABC AB = Ac (Isosceles D) -(1) BC = 48 cm The perimeter of D ABC = AB + BC + CA AB + 48 + AC AB + 48 + AC = 108 But AB = AC from (1) \ 2 AC = 108 - 48 Ac = 60/2 = 30 \ AC = AB = 30 cm Draw AD ^ BC which bisect the base BC so that CD = 48/2 = 24 cm In AC = ADC AC = 30, CD = 24, AD = ? I right angle D ADC AD² = AC² - CD² {Pythagaras theorem} = (30)² - (24)² = 900 - 576 = 324 AD = Ö324 = 18 \ Area of DABC = 1/2 x base x height = 1/2 x 48 x 18 = 432 sq cm.

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