Question

If a room was 2m longer and 3 m broader, its area would have been increases by 75 sq.m. If it were 1 m shorter and 2 m broader, the area would have increased by 16 sq.m. Find it's length and breadth​

Answer 1

Answer:  The length and breadth of the room are 15 m and 12 m respectively.

Step-by-step explanation:  Given that is a room was 2 m longer and 3 m broader, its area would have been increases by 75 sq.m.

If it were 1 m shorter and 2 m broader, the area would have increased by 16 sq.m.

We are to find the length and breadth of the rectangular room.

Let x m and y m represents the length and breadth of the room.

According to the given information, we have

$(x+2)(y+3)=xy+75\\\\\Rightarrow xy+3x+2y+6=xy+75\\\\\Rightarrow 3x+2y=69~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$(x-1)(y+2)=xy+16\\\\\Rightarrow xy+2x-y-2=xy+16\\\\\Rightarrow 2x-y=18\\\\\Rightarrow 4x-2y=36~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Adding equations (i) and (ii), we get

$(3x+2y)+(4x-2y)=69+36\\\\\Rightarrow 7x=105\\\\\Rightarrow x=\dfrac{105}{7}\\\\\Rightarrow x=15.$

Substituting the value of x in equation (i), we get

$3\times15+2y=69\\\\\Rightarrow 2y=69-45\\\\\Rightarrow 2y=24\\\\\Rightarrow y=\dfrac{24}{2}\\\\\Rightarrow y=12.$

Thus, the length and breadth of the room are 15 m and 12 m respectively.

Answer 2

Step-by-step explanation:

x=15

x=15y=12

x=15y=12SEE THE ATTACHMENT

x=15y=12SEE THE ATTACHMENTSTEP BY STEP

x=15y=12SEE THE ATTACHMENTSTEP BY STEPAND MARK AS BRAINLIST