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
Find the dimensions of the rectangle.​

Answer 1

✬ Length = 18 cm ✬

✬ Breadth = 15 cm ✬

Step-by-step explanation:

Given:

• Length of rectangle is greater than breadth by 3 cm.
• Area remains same , after increasing & decreasing length and breadth by 9 and 5 cm respectively.

To Find:

• Dimensions of rectangle ?

Solution: Let the breadth of rectangle be x cm. Therefore,

➼ Length will be = 3 more than x

➼ Length = (x + 3) cm

As we know that

★ Ar. of Rectangle = Length × Breadth ★

$\implies{\rm }$ (x + 3) × x

$\implies{\rm }$ x² + 3x

• So the area is x² + 3x

Now , A/q

• New length = x + 3 + 9 = (x + 12) cm

• New breadth = (x – 5) cm

• New area = Old area

➟ New (Length × Breadth) = x² + 3x

➟ (x + 12) (x – 5) = x² + 3x

➟ x(x – 5) + 12(x – 5) = x² + 3x

➟ x² – 5x + 12x – 60 = x² + 3x

➟ 7x – 3x = 60

➟ 4x = 60

➟ x = 60/4 = 15 cm

So,

• Breadth is x = 15 cm

• Length is (x + 3) = 15 + 3 = 18 cm

Answer 2

Answer:

Given :-

• Length of rectangle is greater than breadth by 3 cm.
• Area remains same , after increasing & decreasing length and breadth by 9 and 5 cm.

To Find :-

Dimensions

Solution :-

Let the breadth be x and length be x + 3

As we know that

Area = Length × Breadth

Area = x × x + 3

Area = x² + 3

Now,

New length = x + 12 cm

New breadth decreased by 5 = x - 5

(x + 12) (x - 5) = x² + 3x

x(x - 5) + 12(x - 5) = x² + 3x

x² - 5x + 12x - 60 = x² + 3x

-5x + 12x - 60 = 3x

7x - 60 = 3x

7x - 3x = 60

4x = 60

x = 60/4

x = 15 cm

Now,

Breadth = 15 cm

Length = x + 3 = 15 + 3 = 18