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

Given:

The length of a rectangle is greater than the breadth by 3cm, if the length is increased by 9cm & breadth is reduced by 5cm, the area remains same.

To find:

The dimensions of the rectangle.

\bf{\Large{\underline{\rm{\red{Explanation\::}}}}}

We know that area of rectangle= [length × breadth] [sq.units]

Let the length be R cm &

Breadth be (R - 3)cm

A/q,

The length is increased by 9cm & breadth is reduced by 5cm;

New length formed of rectangle= (R+9)cm

New breadth formed of rectangle= (R-3-5)cm = (R-8)cm

The area remains the same;

⇒ Length × Breadth = New length × New breadth

⇒ R(R-3) = (R+9)(R-8)

⇒ R² - 3R = R² -8R + 9R - 72

⇒ \cancel{R^{2}} -3R=\cancel{R^{2}} -8R+9R-72

⇒ -3R = -8R + 9R -72

⇒ -3R = R - 72

⇒ -3R -R = -72

⇒ -4R = -72

⇒ R = \cancel{\frac{-72}{-4} }

⇒ R =18cm

Now,

The dimensions of the rectangle:

Length of the rectangle,[R]= 18cm

Breadth of the rectangle,[R-3]= (18-3)cm= 15cm.

Answer 2

Answer:

• Length = 18 cm
• Breadth = 15 cm

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