[ since, the diagonal of rhombus bisects each other at 90°] => OQ2 = PQ2 – OP2 = (10)2 – (8)2 Hence, the length of its hypotenuse is √32 cm. The area of a triangle with base 4 cm and height 6 cm is 24 cm2. If the area of an equilateral triangle is 16√3 cm2, then the perimeter of the triangle is Thinking process • Also, area of parallelogram ABCD =Base x Altitude AC2 = AB2 + BC2 = 42 + 42 = 16 + 16 Solution: Question 4: 918. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. Points, lines, line segments, and planes. Solution: Question 9. Solution: Question 9: Solution: Cloudflare Ray ID: 616aa280a829ee0f If (a, b) is the mid-point of the line segment joining the points A (10, -6), B (k, 4) and a – 2b = 18, find the value of k and the distance AB. We know that, area of a triangle=½ (Base x Height) Let the coordinates of fourth vertex be D (x, y) In a parallelogram, diagonals bisect each other. 2. Area of an equilateral triangle = √3/4 (Side)2 = (√3/4) x 20 x 20 = 100 √3 m2 Also, find the length of the altitude from vertex A on the side DC. Thinking Process Without using the distance formula, show that the points A (4, 5), B (1, 2), C (4, 3) and D (7, 6) are the vertices of a parallelogram. Question 7. As you drag any vertex, you will see that the trapezoid redraws itself keeping the height and bases constant. Here Base = 4 cm and Height = 6 cm Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Show by section formula that the points (3, – 2), (5, 2) and (8, 8) are collinear. The perimeter of a triangle is 50 cm. (d) Let each side of an equilateral be x. Get RD Sharma Solutions for Class 9 Chapter Quadrilaterals here. 9th grade math lessons are planned and introduce in different activities. Solution: A parallelogram has two pairs of opposite sides that are parallel and equal in length. [∴ base = height, as triangle is an isosceles triangle] True Solution: Question 4: => x = 420/21 = 20 m. Question 8: Solution: Question 10. [taking positive square root because side is always positive] Area = ½ x Base x Altitude => 8 = ½ (Base x Base) Simple Amortization Calculation Formula. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. 4 costs to plough 1 m2 of the field, find the total cost of ploughing the field. Solution: 2000 per m2 a year. Area of regular hexagon of side a = Sum of area of the six equilateral triangles. = 3√3 = 3 x 1.732 = 5.196 cm2 (ii) Using relation, area of parallelogram ABCD =2 (Area of ΔBCD) (a) √32 cm                       (b) √16 cm                      (c) √48 cm                    (d) √24 In figure, ΔABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. (a) 1322 cm2               (b) 1311 cm2                       (c) 1344 cm2                               (d) 1392 cm2 Solution: Solution: Given, side of an equilateral triangle be 8 cm. Find the lengths of its two parallel sides, if one side is 4 cm greater than the other. Solution: Let A (3, 4), B (3, 8) and C (9, 8) be the given points. ∴ Length of inner-rectangle, EF = 40 – 3 – 3 = 34 m and breadth of inner-rectangle, FG =15 – 2 – 2 = 11 m Solution: Question 3: Either of the two combinations (a1 = − 13 , b1 = − 23 , a2 = 1, b2 = 12 ) and (a1 = 1, b1 = 12 , a2 = − 31 , b2 = − 23 ) also satisfies the fifth equation [note that the two alternative pairings do not do so]. Thus, the area of triangle is 100√3 m2. 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The formula for calculating the payment amount is shown below. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. Area of an isosceles triangle = ½ (Base x Height) Question 7: P = initial Principal (loan amount) r = interest rate per period. Solution: Let the point B(5,2) divides the line joining A(3,-2) and C(8,8) in the ratio m:n. Then by section formula, x = (mx 2 +nx 1)/(m+n) 5 = (m×8+n×3)/(m+n) 5 = (8m+3n)/(m+n) 5m+5n = 8m+3n. Solution: Question 7: => OQ2 =100 – 64 = 36 BeTrained.in has solved each questions of RD Sharma very thoroughly to help the students in solving any question from the book with a team of well experianced subject matter experts. Your IP: 149.202.185.114 Given three of vertices of a parallelogram are A(1,2), B (4,3), C (6,6). Solution: Question 8: In trapezium ABCD, we draw a perpendicular line CE to the line AB. Find the total area of the design and the remaining area of the tiles. By section formula, => 9a – 9 = 0 a = 1. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. ∴ Area of a triangle ABC = ½ (Base x Height) = ½ x AC x AB=½ x 4 x 4=8 cm2. How much rent did it pay? The length of its hypotenuse is n = total number of payments or periods. A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs. Find the ratio in which the point P(-1, y) lying on the line segment joining A(-3, 10) and B(6, -8) divides it.