Question

Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given:
(i) Area:25a²-35a+12
(ii) Area:35y²+13y-12
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Answer 1

Step-by-step explanation:

Given :-

i) Area:25a^2-35a+12

(ii) Area:35y^2+13y-12

To find :-

Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given: ?

Solution :-

I) Given that

Area of a rectangle = 25a^2-35a+12

It can be written as

=> 25a^2 - 20a - 15a + 12

=> 5a ( 5a - 4 ) - 3 ( 5a - 4 )

=> ( 5a - 4 ) ( 5a - 3)

It is in the form of Length × Breadth

So the possible expressions for the measurements of the length and breadth are

( 5a - 4 ) ( 5a - 3)

-------------------------------------------------------------

ii) Given that

Area of a rectangle = 35y^2+13y-12

It can be written as

=> 35y^2 + 13y -12

=> 35y^2 -15y + 28y - 12

=> 5y ( 7y -3 ) +4 ( 7y - 3)

=> ( 7y - 3 ) ( 5y + 4 )

It is in the form of Length × Breadth

So the possible expressions for the measurements of the length and breadth are

( 7y - 3 ) ( 5y + 4 )

-------------------------------------------------------------

Answer:-

(I) The possible expressions for the measurements of the length and breadth are

( 5a - 4 ) ( 5a - 3)

(ii)The possible expressions for the measurements of the length and breadth are

( 7y - 3 ) ( 5y + 4 )

Used Method:-

• Splitting the middle term

Used formulae:-

• Length of a rectangle = lb sq.units

Where,

• l = length

• b= breadth

Answer 2

External (pulmonary) respiration : This is the exchange of gases between air spaces of the lungs and blood in pulmonary capillaries. The blood gains O2 and loses CO2.

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