Question

The longth of rectangle exceeds its broadth by 7 cm If the longth is decreased by 4 cm and the breadth is increased by 3 cm, the area of new rectangles
same as the area of the original rectangle. Find the porimotor of rectangle

Answer 1

Answer:

Step-by-step explanation:

B =x

L= x+7

Original Area =x×(x×7)=x^2+7x

New length =x+7-4=x+3

New breadth =x+3

New area =(x+3)(x+3)=x^2+6x+9

A2Q

=x^2+7x =x^2+6x+9

=x^2- x^2+7x=6x+9

=7x-6x=9

=x=9cm=Breadth

9+7=16cm=Length

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Answer 2

The length is 16cm and the breadth is 9cm.

Step-by-step explanation:

We are given that the length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and breadth is increased by 3, the new rectangle is the same Let us start by assuming the breadth of original triangle as the area of the original rectangle.

as x i.e.

$\sf \: breadth \: = x \: \: \: \: \: \: ..(i)$

The length of original rectangle is 7 more than its

breadth, i.e.

$\sf \: length = \: x + 7 \: \: \: \: \: ..(ii)$

From equation (1) and (2) we get the area of the rectangle

as-

$\sf \: Area \: of \: rectangle = length \times breadth$

$\sf \: Area \: of \: rectangle = (x + 7) \times x$

$\sf \: Area \: of \: rectangle = {x}^{2} + 7x \: \: \: \: \: \: ..(iii)$

Now, the lengths and breadth of the rectangle are change

as

$\sf \: Length \: is \: decreased \: by \: 4 \: i.e.$

$\sf \: New \: length (L) = Original \: length +7$

$\sf \: = x + 7 - 4 \\ = \sf \: x + 3 \: \: \: \: \: \: \: ..(iv)$

New breadth (B) = Original breadth +3

$\sf \: (x) + 3 \: \: \: \: \: \: ..(v)$

The area of the rectangle now becomes -

$\sf \: area \: of \: rectangle \: = length \: \times breadth \:$

From equation (4) and (5) we have,

$\sf \: area \: of \: rectangle \: = (x + 3) \times (x + 3)$

Simplifying the above equation we have,

$\sf \: area \: of \: rectangle \: = {x}^{2} + 3x + 3x + 9$

$\sf \: area \: of \: rectangle \: = {x}^{2} + 6x + 9 \: \: \: \: \: \: ..(vi)$

It is given that the equation area remains the same.

Therefore,

From equation (3) and (6) we get,

$\sf \: \: \: \: {x}^{2} + 6x + 9x = {x}^{2} + 7x$

Subtracting both sides by x²

$\sf \: 6x + 9 = 7x$

Subtracting both sides by 6x we get,

$\sf \: \: 9= x$

Therefore, putting the value of x in equation (1) and two we get the length and breadth as follow -

$\sf \: b = x= 9 And,$

$\sf \: 1 = x + 7 = 9 + 7 = 16$

Therefore, the length is 16cm and the breadth is 9cm.