Question

The length of the rectangle exceeds its breadth by 3 cm. If the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70 sq. cm more than that of the given rectangle. Find the length and breadth of the given rectangle.

Answer 1

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Answer 2

Concept:

A rectangle is a 2D shape having four sides and opposite sides are equal.

Given:

The length of the rectangle is 3 more than the breadth,

And,

If the length and breadth both increased by 2 cm, then the area of the new rectangle will be 70 sq. cm more than that of the given rectangle.

Find:

We are asked to find the length and breadth of the given rectangle.

Solution:

We have,

The length of the rectangle is 3 more than the breadth,

Now,

Let,

Breadth = a

So,

Length = 3 + a

Now,

Area of given rectangle  = length × breadth = a × (3 + a) = 3a + a²

According to the question,

If the length and breadth both increased by 2 cm, then the area of the new rectangle will be 70 sq. cm more than that of the given rectangle.,

i.e.

Breadth = a + 2

So,

Length = 3 + a + 2 = 5 + a

Now,

Area of rectangle  = 70 + Area of given rectangle

i.e.

(5 + a) × (a + 2)  = 70 + 3a + a²

i.e.

5a + 10 + a² + 2a  = 70 + 3a + a²

On solving we get,

4a = 70 - 4

i.e.

4a = 60

i.e.

a = 15 cm

i.e. Breadth = 15 cm

So,

Length = 15 + 3 = 18 cm

Hence, the length and breadth of the rectangle are 15 cm and 18 cm.

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