Question
The area of an isosceles triangle ABC is 8√5 cm². In
this triangle, sides AB and BC are equal in length, and the base AC has a length of 8 cm. Determine the perimeter of triangle ABCSolution
Let AB = BC = 'x' cm Area of isosceles triangle = {(c/4) X √(4a2 - c2)} [Where 'a' is the length of two equal sides and 'c' is the length of third (unequal) side] 8√5 = (8/4) X {√(4 X x2 - 82)} Or, (4√5) = √(4x2 - 64) Squaring both sides. (16 X 5) = 4x2 - 64 Or, 144 = 4x2 Or, x2 = 36 So, x = 6 cm (Since, length cannot be negative therefore, we will take the positive root only) So, required perimeter = 6 + 6 + 8 = 20 cm
Pipe ‘A’ fills a tank in 25 hours, and pipe ‘B’ empties it in 50 hours. If both are opened together, how much time will it take to fill 80% of ...
With a bucket full of water, a tank can be filled with 16 buckets. When each bucket holds 12.5 liters of water, how many buckets of 10-liter capacity ca...
Pipe ‘A’ can fill a tank in 20 hours while pipe ‘B’ takes 30 hours to empty it. Pipe ‘A’ is opened alone when the tank was empty and after 1...
A cistern has two pipes. One can fill it with water in 16 hours and other can empty it in 10 hours. In how many hours will the cistern be emptied if bo...
Two pipes A and B can fill a tank in 12 min., and 16 min, respectively. If both the pipes are opened simultaneously, after how much time A should be cl...
Two pipes A and B can fill a tank in 24 min., and 32 min, respectively. If both the pipes are opened simultaneously, after how much time B should be clo...
Pipe E can fill a pool in 24 hours and pipe F in 48 hours. If both the pipes are opened in an empty pool, how much time will they take to fill it?
An inlet tap alone can fill a tank in 40 minutes. However, when both an inlet and an outlet tap are open together, the tank takes 66 (2/3) minutes (or 2...
Pipes A and B can fill a tank in 43.2 minutes and 108 minutes, respectively. Pipe C can empty it at 3 litres/minute. When all the three pipes are opened...
A tank is filled with three pipes A, B, and C. Pipe A takes 18 hr. to fill 60% of the tank and Pipe B takes 8 hr. to fill 40% of the tank. Pipe A and Pi...
Relevant for Exams:
