Question

a rectangle has the same area as another whose length is 6m more and breadth is 4m less. it has also the same area as the third whose lengt
h is 8m more and breadth 5m less. find the length and breadth of the original rectangle.​

Answer 1

Length of original rectangle=24 m

Breadth of original rectangle=20 m

Step-by-step explanation:

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

Area of rectangle=$length\times breadth$

Area of original rectangle=xy

Length of rectangle=x+6

Breadth of rectangle=y-4

Area of rectangle=$(x+6)(y-4)$

Area of rectangle=$xy-4x+6y-24$

According to question

$xy-4x+6y-24=xy$

$-4x+6y-24=0$

$4x-6y=-24$

$2x-3y=-12$...(1)

For second case

$(x+8)(y-5)=xy$

$xy-5x+8y-40=xy$

$5x-8y=-40$....(2)

Using elimination method

Equation(1) multiply by 5 and equation (2) multiply by 2 and then subtract equation(2) from equation (1)

$y=20$

Substitute y=20 in equation (1)

$2x-60=-12$

$2x=-12+60=48$

$x=24$

Length of original rectangle=24 m

Breadth of original rectangle=20 m

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