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In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues uptofive times. What is the ratio of the area of fourth triangle to that of sixth triangle? (Original triangle is counted as 1st triangle)
A circle of maximum area is inscribed in the square. An equilateral triangle is inscribed in that circle and all the vertices of the triangle touch the circle. A triangle is formed by the joining of the midpoint of the sides of the equilateral triangle. Find the ratio of the area of the square and area of the triangle which is formed by midpoints.
Road damage is often down to a few factors such as the quantity of traffic, the weight of the vehicles passing on it, and environmental conditions. XYZ town has a port, called ABC. To get to ABC, there is a road, that is divided into two lanes. One for the traffic going towards ABC port, and the other for traffic going away from ABC port. The lane of the road that leads to ABC port, has significantly less damage, than the lane that leads away from it. Which of the following helps explain this best?
In the following question, 3 statements are given. You have to find which is/are necessary and sufficient to answer the following question.  Find the area of the Triangle ABC Statement I∶ Perimeter of the triangle is 100. Statement II∶ Sum of the largest and smallest side of the triangle is 73. Statement III∶ The triangle is an isosceles triangle.
In a triangle ABC, parallel lines are drawn to each side cutting the other two sides at the mid points. A new triangle is formed inside the original triangle. Find the ratio of the perimeter of the new triangle to perimeter of the ABC.
Triangle XYZ is similar to triangle RST. Area of triangle XYZ is 2304 cm2 and area of triangle RST is 1296 cm2. If the longest side of the triangle XYZ measures 144 cm, then what will be the measure of the longest side of the triangle RST?
Consider the following statements : I. Every equilateral triangle is necessarily an isosceles triangle. II. Every right-angled triangle is necessarily an isosceles triangle. III. A triangle in which one of the median is perpendicular to the side it meets, is necessarily an isosceles triangle. The correct statements are:
Consider the following statements :I. Every equilateral triangle is necessarily an isosceles triangle.II. Every right-angled triangle is necessarily an isosceles triangle.III. A triangle in which one of the median is perpendicular to the side it meets, is necessarily an isosceles triangle.The correct statements are:
In the given figure, ABC is a right-angle triangle, AB = 12 cm and AC = 15 cm. A square is inscribed in the triangle. One of the vertices of square coincided with the vertex of triangle. What is the maximum possible area (in cm2) of the square?
ABC is a triangle with vertices (x, y), (y, x) and (x/2, y/2). The x coordinate of centroid of the triangle is 25% more than y coordinate of the centroifd of the triangle. What is the value of x/y?