Question

please help!!!!!
if the length of a rectangle is increased by 7 m and the breadth is decreased by 3 m its area remain unchanged similarly if the length is decreased by 7 m and the breadth is increased by 5 m, still area remains unchanged. Find the length and the breadth of the rectangle

Answer 1

Let :

• Initial length = x
• Initial breadth = y
• Area of rectangle = xy

Given :

• Length is increased by 7 m and the breadth is decreased by 3 m its area remain unchanged
• length is decreased by 7 m and the breadth is increased by 5 m, still area remains unchanged.

Formula used :

• Area of rectangle = length×breadth

Solution :

First case,

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

=> xy -3x + 7y - 21 = xy

=> 7y - 3x - 21 = xy-xy

=> 7y - 3x - 21 = 0 ........... equation 1

Second case,

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

=> xy + 5x - 7y -35 = xy

=> 5x - 7y - 35 = xy - xy

=> 5x - 7y - 35 = 0 ........... equation 2

On Adding equation 1 & 2 , we get

=> (7y - 3x - 21 ) + ( 5x - 7y - 35) = 0+0

=> 7y - 7y + (5x - 3x) - (21+35) = 0

=> 2x - 56 = 0

=> 2x = 56

=> x = 56/2

=> x = 28

Putting value of x, in equation 1 [ 7y - 3x - 21 = 0] we get;

=> 7y - 3(28) - 21 = 0

=> 7y = 21 + 84

=> 7y = 105

=> y = 105/7

=> y = 15

ANSWER :

• Length = x = 28m
• Breadth = y = 15cm