Question

the length of a rectangle exceeds it's breadth by 3cm. if the length and breadth are each increased by 2cm, then the area of the new rectangle will be 70cm square more than the original. find length and breadth​

Answer 1

Answer:

here,

breadth=x+2

length=x+2+3=x+5

according to the question,

area of rectangle=l×b

=(x+2)(x+5)

=x2+5x+2x+10

=x2+7x+10

Answer 2

Given : -

• Length of a rectangle exceeds it's breadth by 3cm.
• If the length and breadth are each increased by 2cm, then the area of the new rectangle will be 70cm square more than the original.

To Find :-

• Length
• Breadth

Solution :-

Acc. to 1st condition :

Let the length be x and breadth be x + 3.

Area of rectangle = L × B

= x × (x + 3)

= x² + 3x

Acc. to 2nd condition :

Length of rectangle = x + 2

Breadth of rectangle = x + 3 + 2

= x + 5

Area of rectangle = (x + 2) (x + 5)

Given that, new area formed is 70 cm² more than the original area.

(x + 2) (x + 5) = 70 + x² + 3x

x² + 5x + 2x + 10 = 70 + x² + 3x

x² + 7x + 10 = 70 + x² + 3x

x² - x² + 7x - 3x = 70 - 10

4x = 60

$x = \frac{60}{4}$

x = 15

Length of rectangle = 15 cm

Breadth of rectangle = 15 + 3 = 18 cm.

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