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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)
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 up to seven times. What is the ratio of the area of fourth triangle to that of seventh triangle?
Consider the following statements: I. If three equal circles are drawn on the vertex of equilateral triangle in such a way that all the circles touch each other externally then the triangle is equilateral triangle. II. The circum centre of any triangle cannot be lie on its side.
In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. the length of the smallest side of the triangle PQR is:
In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :
Calculate the number of equilateral triangle that can be produced by melting and recasting a metallic sphere having a radius equal in length to the side of equilateral triangle.  (The equilateral triangle and sphere are having uniform thickness and also there is no loss of material in melting and recasting).
The midpoints of the sides of an equilateral triangle PQR are X, Y and Z if the perimeter of triangle PQR is 24 cm, then what is the perimeter of triangle XYZ?.
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.
PQR is an equilateral triangle. MN is drawn parallel to QR such that M is on PQ and N is on PR. If PN = 6 cm, then the length of MN is:
PQR is a triangle in which PQ = PR. QR is produced to point S. T is a point on PR and U is a point outside the triangle. TU is parallel to PQ and PU is parallel to QR. If angle ∠PQR = 70° and ∠PUS = 150°, find the value of ∠USR.