Question
The area of an equilateral triangle is given as 432
β3βcm2 . A square is constructed such that one of its sides is equal to the height of the triangle. Calculate the difference between the perimeters of the square and the triangle.Solution
Area of equilateral triangle = (β3/4) X side2 Let the side of the given triangle be 'a' cm. ATQ; 432β3 = (β3/4) X a2 Or, 432 X 4 = a2 So, 'a' = Β± 24β3 Since, side cannot be negative, a = +24β3 Height of equilateral triangle = (β3/2) X side So, height of the given triangle = (β3/2) X 24β3 = 36 cm So, length of each side of the square = 36 cm So, perimeter of the square = 36 X 4 = 144 cm And perimeter of the triangle = 24β3 X 3 = 72β3 cm So, required difference = 144 - 72β3 = 72(2 - β3) cm
In what ratio coffee at 325 Rs/kg should be mixed with the coffee at 375 Rs/kg so that after mixture its rate become 340 Rs/kg if the quantity of 1st ty...
If sinA = 3/5 and cosB = 12/13, where A and B are in the first quadrant, find sin(A + B).
A merchant has 1200 kg of sugar, part of which he sells at 9% profit and the rest at 15% profit. He gains 11% on the whole. The quantity (in kg) sold at...
The Average weight of 12 students in the class is 38 kg, when 4 new students included, the average weight becomes 39.5 kg and the weight of those 4 stu...
In what ratio must a person mix three kinds of rice costing him Rs 1.16,Rs 1.40 and Rs 1.72 per Kg so that the mixture may be worth Rs 1.37 per Kg?
A and B together can complete a work in 12 days. B and C together can complete the same work in 15 days, and A and C together can complete it in 20 days...
4, 14, 44, 134, ?, 1214
One type of liquid contains 15% of benzene, the other contains 20% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the secon...
A shopkeeper has 76 kg rice a part of it, he sells at the profit of 48% and rest at loss of 28% and he get the loss of 16% so what is the quantity sold ...
A luxury watch is originally priced at βΉ15,000. During a seasonal sale, the watch is offered at a discount of 30%. After the discount, an additional 1...