Question

the length of a rectangle exceed it's breath by 3cm if they are each increased by 3cm the area of the new rectangle will be 84 cm sq more than that of the given rectangle. Find the dimensions of the rectangle

Answer 1

let breadth of rectangle be x
length be x+3
Now area is (x) .(x+3)
...................
Now breadth = x+3
length = x+6
Area is (x+3).(x+6)
ATQ...
(x+3.x+6)-(x. x+3)=84 cm²
(x²+6x+3x+18)-(x²+3x) =84cm²
x²+6x+3x+18-x²-3x=84cm2
6x+18=84cm²
x+3=14
x=14-3
x=11cm
Breadth = 11cm
Length =14cm

If satisfied with answer mark it as brainliest

Answer 2

Hey Mate,

Given,

=> The Length exceeds the Breadth by 3 cm.

=> If both Length and Breadth are increased by 3 cm, then the new area will be 84 sq. cm more than the original area.

Now,

We can write Length as ( Breadth + 3 )

( Since, it is given that length exceeds breadth by 3 cm )

Let us Write Breadth as "B".

We also know that the area of a rectangle = Length * Breadth

Then,

=> Area of the Rectangle = B * ( B + 3 )

Now, It is given that if both Length and Breadth are increased by 3 cm then, the area also increases by 84 sq. cm.

Then,

=> Area of the Rectangle + 84 = ( B + 3 ) * ( B + 6 )

So, on subtracting the old equation from the new equation, we get :-

=> Area + 84 sq. cm - Area = ( B + 3 ) * ( B + 6 ) - ( B ) * ( B + 3 )

=> 84 sq. cm = $( B^{2} + 6B + 3B + 18 ) - ( B^{2} + 3B )$

=> 84 sq. cm = $B^{2} + 6B + 3B + 18 -  B^{2} - 3B$

=> 84 sq. cm = $6B + 18$

=> ( 84 - 18 ) cm = 6B

=> 66 cm = 6B

=> ( 66 / 6 ) cm = B

=> Breadth = 11 cm

So, Length = ( 11 + 3 ) cm = 14 cm

Therefore, the Length of the Rectangle is equal to 14 cm, whereas the Breadth is equal to 11 cm.

Hope My Answer Brings A Smile On Your Face

^_^