Question

The diagonals of a rectangle are given by 4x - 5y = 1 and 4x + 5y = 11 and one of the vertex is at (4, -1). On the basis of above informations, answer the following questions : The area of the rectangle (in sq. units) is equal to -​

Answer 1

Answer:

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Answer 2

Given:

The diagonals of a rectangle are given by 4x - 5y = 1 and 4x + 5y = 11 and one of the vertex is at (4, -1). Based on the above information, answer the following questions

To Find:

The area of the rectangle (in sq. units) is equal to -​

Solution:

We are given the diagonals of the rectangle and one of the vertexes also we can find the value of the other vertex using the midpoint formula and when we have two vertices then the other two can also be found because if say (a,b) and (b,c) are two vertices point on one diagonal then the points of the other two will be (a,c) and (b,b)

Hence, solving both the equations,

$4x - 5y = 1 \\ 4x + 5y = 11$

we have the intersection as (1.5,1)

Now using the midpoint formula the value of another vertex will be,

1.5=(4+x)/2

x=-1

similarly, for y, we get

y=3

The points are (4,-1) and (-1,3) so the value of the other vertex is (4,3) from here we can find the value of length and breadth

Length=5 units

Breadth=4units

So the area will be

Area=4*5

       =20sq.units

Hence, the area of the rectangle is 20sq.units.