Question

the breadth of a rectangle is 3 less than the length. if bot the length and breadth are reduced by 3 units, the area of the rectangle reduces by 90sq. units

Answer 1

DIAGRAM:

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ANSWER:

• Length = 18 units

• Breadth = 15 units.

GIVEN:

• Breadth of the rectangle is 3 less than the length.

• If both the length and breadth are reduced by 3 units, the area of the rectangle reduced by 90 sq. units.

TO FIND:

• The length and breadth of the rectangle.

EXPLANATION:

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

Area of rectangle (A) = l × b

l = x

b = x - 3

A = x(x - 3)

A = x² - 3x

Area of rectangle (A') = l' × b'

If the length and breadth are reduced by 3 units

l' = x - 3

b' = x - 6

A' = x - 3(x - 6)

A' = x² - 3x - 6x + 18

A' = A - 90

x² - 9x + 18 = x² - 3x - 90

- 9x + 18 = - 3x - 90

Divide by 3 on both sides

- 3x + 6 = - x - 30

- 2x = - 36

x = 18 units

x - 3 = 15 units

∴ Length = 18 units and Breadth = 15 units.

VERIFICATION:

Area of rectangle (A) = l × b

l =  x = 18

b = x - 3 = 18 - 3 = 15

A = 18 × 15

A = 270

Area of rectangle (A') = l' × b'

l' = x - 3 = 18 - 3 = 15

b' = x - 6 = 18 - 6 = 12

A' = 15 × 12

A' =  180

A - A' = 270 - 180 = 90

HENCE VERIFIED.

Answer 2

First Condition :

The breadth of a rectangle is 3 less than the length

Let

Length of rectangle be " x "

Breadth = " x - 3 "

Thus ,

Area = (x) × (x - 3) = (x)² - 3x

Second Condition :

if both the length and breadth are reduced by 3 units, the area of the rectangle reduces by 90 sq. units

Thus ,

(x - 3) × (x - 3 - 3) = (x)² - 3x - 90

(x)² - 3x - 3x - 3x + 9 + 9 = (x)² - 3x - 90

-6x + 18 = -90

-6x = -108

x = -108/-6

x = 18 units

$\therefore$ The length and breadth of rectangle are 18 units and 15 units