Home
Class 12
MATHS
Let S be the square of unit area. Consid...

Let S be the square of unit area. Consider any quadrilateral which has one vertex on each side of S. If a, b, c and d denote the lengths of the sides of the quadrilateral, prove that `2 le a^(2)+b^(2)+c^(2)+d^(2)le 4`.

Promotional Banner

Similar Questions

Explore conceptually related problems

If a,b,c,d are the side of a quadrilateral, then find the the minimuym value of (a^(2)+b^(2)+c^(2))/(d ^(2))

If g, h, k denotes the side of a pedal triangle, then prove that (g)/(a^(2))+ (h)/(b^(2))+ (k)/(c^(2))=(a^(2)+b^(2) +c^(2))/(2 abc)

An equilateral triangle is inscribed in the parabola y^(2) = 4ax , where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

Consider a DeltaABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C, repectively. if a=1,b=3 and C=60^(@), then sin ^(2) B is equal to

If l, m, n denote the side of a pedal triangle, then (l)/(a ^(2))+(m)/(b^(2))+(n)/(c ^(2)) is equal to

Find the area of quadrilateral ABCD with vertices A(-4, -2), B(-3, -5), C(3,-2) and D(2,3).

The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the angle between them is 60^0dot If the area of the quadrilateral is 4sqrt(3) , find the remaining two sides.

In DeltaABC, /_B=90^(@) . D and E are any points on sides AB and BC respectively. Prove that AE^(2)+CD^(2)= AC^(2)+DE^(2) .

Consider a Delta ABC and let a,b, and c denote the leghts of the sides opposite to vertices A,B and C, respectively. Suppose a=2,b =3, c=4 and H be the orthocentre. Find 15(HA)^(2).