Question

the area of a rectangle remains the same if the length is increased by 7 meters and the breadth is decreased by 3m . The area remains unaffected if the length is decreased by 7m and breadth is increased by 5m. find the dimensions of rectangle

Answer 1

This picture will help you......

Answer 2

Concept

The area of the rectangle is the product of the length with breadth. Mathematically it is written as

A=length * breadth

We will make the two linear equations and then solve it two find the length and breadth of the given rectangle.

Given

The area of the given rectangle remains constant after decreasing or increasing the length or breadth.

Find

We are asked to calculate the value of the length and breadth of the rectangle.

Solution

Let x is the length and y is the breadth of the rectangle.

From the first condition, we have

xy = (x + 7) (y - 3)

3x - 7y = -21 ...(1)

And similarly from the second condition we have,

xy = (x - 7)(y + 5)

5x - 7y = 35 ...(2)

Now subtracting the equation (1) from equation (2), we have

2x = 35 + 21

x = 28

Putting the value of x into the equation (1), we get

(3*28) - 7y = -21

y = 15

Hence the length and breadth of the rectangle is 28 m and 15 m respectively.

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