Question

14 The length of a rectangle is greater than the breadth by 3 cm. If the length is
increased by 9 cm and the breadth is reduced by 5 cm, the area remains the same
and breadth of the
Find the dimensions of the rectangle​

Answer 1

Given:

✰ The length of a rectangle is greater than the breadth by 3 cm.

✰ If the length is increased by 9 cm and the breadth is reduced by 5 cm, the area remains the same.

To find:

✠ The length of a rectangle

✠ The breadth of a rectangle

Solution:

Let the breadth of a rectangle be x cm

then, length of a rectangle will be 3 cm greater than breadth = ( x + 3 ) cm

Area of a rectangle = length × breadth

⟹ Area of a rectangle = l × b

⟹ Area of a rectangle = x × ( x + 3)

⟹ Area of a rectangle = x² + 3x cm²

Now, If the length is increased by 9 cm ( here we will add length by 9 cm = (x + 3 + 9)cm = ( x + 12 ) cm ) and the breadth is reduced i.e, decrease by 5 cm ( here we will substract 5 cm from it's breadth (x - 5) cm ), then the area remains the same.

We have,

⟹ Area of a rectangle = ( x + 12 ) × (x - 5)

⟹ Area of a rectangle = x(x - 5) 12(x - 5)

⟹ Area of a rectangle = x² - 5x + 12x - 60

⟹ Area of a rectangle = x² + 7x - 60 cm²

Now, we know that the area remains the same in both the cases, so

According to question,

➤ x² + 3x = x² + 7x - 60

➤ x² - x² + 3x - 7x = - 60

➤ - 4x = - 60

➤ 4x = 60

➤ x = 60/4

➤ x = 15

∴ The breadth of a rectangle = 15 cm

Now,

⇾The length of a rectangle = ( x + 3 ) cm

⇾The length of a rectangle = ( 15 + 3 ) cm

⇾The length of a rectangle = 18 cm

∴ The length of a rectangle = 18 cm

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