Question

a and b real numbers between 0 and 1 A(a, 1), B(1, b) andC(0, 0) are the vertices of triangle

1:- If the triangle ABC is equilateral, its area is equal to

Solution

Correct option is

a2 +1 = b2 + 1 = (a – 1)2 + (b – 1)2

⇒   a = b [as 0 < a, b < 1]and   

     2(a2 – 2a + 1) = a2 + 1 ⇒ a2 – 4a + 1 = 0

, area of the triangle

         

SIMILAR QUESTIONS

Q1

Given two points A(-2, 0) and B(0, 4), M is a point with coordinates (xx), x  0. P divides the joint A and B in the ratio 2 : 1 . C and D are the mid-points of BM and AM respectively. Find the perimeter of the quadrilateral ABCD. Find the ratio of the areas of the triangles APM and BPM .

Q2

Given two points A(-2, 0) and B(0, 4), M is a point with coordinates (xx), x  0. P divides the joint A and B in the ratio 2 : 1 . C and D are the mid-points of BM and AM respectively. Find the perimeter of the quadrilateral ABCD.

Q3

Given two points A(-2, 0) and B(0, 4), M is a point with coordinates (xx), x  0. P divides the joint A and B in the ratio 2 : 1 . C and D are the mid-points of BM and AM respectively. Find the perimeter of the quadrilateral ABCD. Find the area of the quadrilateral ABCD in units.

Q4

A(p, 0), B(4, 0), C(5, 6) and D(1, 4) are the vertices of a quadrilateral ABCD If  is obtuse, the maximum integral value of p is

Q5

The value of p for which  is obtuse and  is a right angle is

Q6

A(p, 0), B(4, 0), C(5, 6) and D(1, 4) are the vertices of a quadrilateral ABCD 

If two sides of the quadrilateral are equal; area of the quadrilateral is

Q7

(0, 0), A(1, 1), B(0, 3) are the vertices of a triangle OAB.divides OB in the ratio 1 : 2, Q is the mid-point of AP, R divides AB in the ratio 2 : 1

1:- If 

Q8

(0, 0), A(1, 1), B(0, 3) are the vertices of a triangle OAB.divides OB in the ratio 1 : 2, Q is the mid-point of AP, R divides AB in the ratio 2 : 1

area of ΔPQR : area of ΔOAB is

Q9

(0, 0), A(1, 1), B(0, 3) are the vertices of a triangle OAB.divides OB in the ratio 1 : 2, Q is the mid-point of AP, R divides AB in the ratio 2 : 1

If S is the mid-point of PR, then QS is equal to

Q10

If the triangle ABC in  isosceles with AC = BC and 5(AB)2 = 2(AC)2 then