Maths

In an equilateral triangle , prove that three times the square of one side is equal to four time the square of one of its altitudes. In an equilateral triangle prove that three times the square of one side is equal to four time the square of one of its altitudes. October 5, 2020 Category: [...]

In an equilateral triangle ABC,D is a point on side BC such that BD = 3/1 BC. Prove that 9 AD^2 = 7AB^2. D is a point on side BC such that BD = 3/1 BC. Prove that 9 AD^2 = 7AB^2. In an equilateral triangle ABC October 5, 2020 Category: Chapter 6 - Triangles [...]

The perpendicular from A on side BC of a ΔABC intersect BC at D such that DB = 3CD. Prove that 2AB^2 = 2AC^2 + BC^2. The perpendicular from A on side BC of a ΔABC intersect BC at D such that DB = 3CD. Prove that 2AB^2 = 2AC^2 + BC^2. October 5, 2020 [...]

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that : AE^2 + BD^2 = AB^2 + DE^2 D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that : AE^2 + [...]

Two poles of height 6m and 11m stands on a plane ground, if the distance between their feet is 12m. Find the distance between their tops. if the distance between their feet is 12m. Find the distance between their tops. Two poles of height 6m and 11m stands on a plane ground October 5, 2020 [...]

An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1 2/1 hours? An aeroplane leaves an [...]

A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut ? 12 cm 5 cm​ Sides of triangles are given [...]

A ladder 10m long reaches a window 8m above the ground. Find the distance of the foot of the ladder from the base of the wall. A ladder 10m long reaches a window 8m above the ground. Find the distance of the foot of the ladder from the base of the wall. October 5, 2020 [...]

In given figure from a point O in the interior of a △ABC, perpendiculars OD, OE and OF are drawn to the sides BC, CA and AB respectively. Show that : (i) AF^2 + BD^2 + CE^2 = OA^2 + OB^2 + OC^2 − OD^2 − OE^2 − OF^2 (ii) AF^2 + BD^2 + CE^2 [...]

Prove that the sum of squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. Prove that the sum of squares of the sides of a rhombus is equal to the sum of the squares of its diagonals. October 5, 2020 Category: Chapter 6 - Triangles , [...]