Question

If three vertices of a rectangular are (0, 0), (a, 0) and (0, b), length of each diagonal is 5 and the perimeter 14, then the area of the rectangle is

Solution

Correct option is

12

       a2 + b2 = 25

     2(a + b) = 14

⇒          ab = 12

SIMILAR QUESTIONS

Q1

Two vertices of a triangle are (–1, 4) and (5, 2). If its centroid is (0, –3), find the third vertex.

Q2

Find the area of the pentagon whose vertices are A(1, 1), B(7, 21), C(7, –3), D(12, 2) and (0, –3).

Q3

Find the locus of a point which moves such that its distance from the point (0, 0) is twice its distance from the – axis.

Q4

Find the equation of the curve 2x2 + y2 – 3+ 5– 8 = 0 when the origin is transferred to the point (–1, 2) without changing the direction of axes.

Q5

Given the equation  through what angle should the axes be rotated so that the term in xy be waiting from the transformed equation. 

Q6

Find the locus of the point of intersection of the lines and  where α is variable.

Q7

Find the locus of a point whose co – ordinate are given by t2= 2+ 1, where is variable.

Q8

The points (a, b + c), (b, c + a) and (c, a + b) are

Q9

O(0, 0), P(–2, –2) and Q(1, –2) are the vertices of a triangle, R is a point on PQ such that PR : RQ 

Q10

If the line joining the points A(a2, 1) and B(b2, 1) is divides in the ratio b : a at the pint P whose x-coordinate is 7, their