Question

the length of a rectangle exceeds its breadth by 4 cm if the length and breadth are increased by 3 cm each the area of the new rectangle will be 18 square is more than that of the given rectangle find the length and breadth of the given rectangle​

Answer 1

Correct Question:

• The length of a rectangle exceeds its breadth by 4 cm if the length and breadth are increased by 3 cm each the area of the new rectangle will be 81 cm² is more than that of the given rectangle find the length and breadth of the given rectangle.

GivEn:

• The length of a rectangle exceeds its breadth by 4 cm.

• If length and breadth are increased by 3 cm each the area of the new rectangle will be 81 cm² is more than that of the given rectangle.

To find:

• Length and breadth of given rectangle?

Solution:

☯ Let breadth of rectangle be x cm.

Therefore, Length of rectangle is (x + 4) cm

We know that,

Area of Rectangle = Length × Breadth

Therefore,

➯ Area of Rectangle = x(x + 4) = x² + 4x

Now,

★ According to the Question:

• If length and breadth are increased by 3 cm each the area of the new rectangle will be 81 cm² is more than that of the given rectangle.

➯ (x + 3)(x + 4 + 3) = x² + 4x + 81

➯ (x + 3)(x + 7) = x² + 4x + 81

➯ x² + 10x + 21 = x² + 4x + 81

➯ 10x + 21 = 4x + 81

➯ 10x - 4x = 81 - 21

➯ 6x = 60

➯ x = 60/6

➯ x = 10

Hence,

• Breadth of rectangle, x = 10 cm
• Length of rectangle, (x + 4) = 10 + 4 = 14 cm.

∴ Hence, Length and Breadth of given Rectangle is 14 cm and 10 cm respectively.

Answer 2

Answer:

$\huge \bf \maltese \clubs \: answer \maltese \clubs$

$\sf \underline {let}$

Breadth of rectangle = x

Length of rectangle = x +4

As we know that

$\huge \boxed { \sf \: area \: = l \: \times b}$

$\sf \: area \: = x(x + 4) = {x}^{2} + 4x$

As we are knowing that when the breadth is x. Hence the length will be x+4. And we the length and breadth increase then the area changes into 18 cm². In this we have to find its length and breadth

Now,

$\sf \implies(x + 3)(x + 4 + 3) = {x}^{2} + 4x + 81$

$\sf \implies(x + 3)(x + 7) = {x}^{2} +4x+81$

$\sf \implies {x}^{2} + 10x + 21 = {x}^{2} + 4x + 81$

$\sf \implies 10x + 21 = 4x + 81$

$\sf \implies10x - 4x = 81 - 21$

$\sf \implies \: 6x = 60$

$\sf \implies \: x = \dfrac{60}{6}$

$\sf \implies \: x \: = 10$

$\huge \bf \: breadth = 10$

$\huge \bf length = 10 + 4 = 14$