The width of a rectangle is to third the length. when each dimension is decreased by 2 cm, the area is decreased by 32 cm period find the dimensions of the original rectangle.

Hey there!!

Basic formula :

Area of a rectangle  = Length × breadth

Given :

Width = two third of the length

Let's take the dimension of the length as ' x '

Then the breadth would be = 2x / 3

Area = ( x ) × ( 2x / 3 )

Area = 2x² / 3

Each dimension is decreased by 2

This states that we will need to add 2 to both length and breadth

Length = x - 2

Breadth = 2x / 3 - 2

= 2x - 6 / 3

Area = ( x - 2 ) × ( 2x - 6 / 3 )

Area = 2x² - 10x + 12 / 3

What they say?

Area is decreased by 32 cm

Which means..

If we add 32 to the new rectangles area , the areas would be equal to the new and the old rectangle

2x² / 3 = ( 2x² - 10x + 12 / 3 ) + ( 32 )

2x² / 3 = 2x² - 10x + 108 / 3

Multiplying by 3 on both sides

2x² = 2x² - 10x + 108

Adding 10x on both sides

2x² + 10x = 2x² + 108

subtracting by 2x² on both sides

10x = 108

Dividing by 10 on bot sides

x = 10.8

Length of the original rectangle = 10.8 cm

Breadth = 2 ( 10.8 ) / 3

= 7.2 cm

Hope my answer helps!

answer:

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answer:

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