Question

A landlord is selling rectangular piece of land whose length and breadth are
$2 {x}^{2} - 3 \: metre$
and
$x + 10$
respectively.

1) what is the degree of polynomial as per the perimeter of the field.
2) find the perimeter and area of the land if the value of the variable given above is 5

​

Answer 1

||✪✪ QUESTION ✪✪||

A landlord is selling rectangular piece of land whose length and breadth are (2x² - 3) and (x+10) respectively.

1) what is the degree of polynomial as per the perimeter of the field. ?

2) find the perimeter and area of the land if the value of the variable given above is 5 ?

|| ★★ FORMULA USED ★★ ||

→ perimeter of Rectangle = 2( Length * breadth).

→ Area or Rectangle = Length * Breadth

→ The degree of polynomials in one variable is the highest power of the variable in the algebraic expression.

|| ✰✰ ANSWER ✰✰ ||

As told above ,

→ Perimeter of Rectangle = 2(2x² - 3 + x + 10) = 2(2x² + x +7) = 4x² + 2x + 14

Here, we can see that, Highest Degree is 2.

So, Degree of polynomial as per the perimeter of the field is 2.

_____________________________

Now, at f(5) we have,

→ Length = f(x) = 2x² - 3 ,

→ f(5) = 2*(5)² - 3

→ f(5) = 2*25 - 3

→ Length = 47 unit.

Similarly Breadth ,

→ Breadth = 5 + 10 = 15 unit.

So ,

→ Perimeter = 2(47 + 15) = 2*62 = 124 units.

And,

→ Area = 47 * 15 = 705 units² .

__________________________

Answer 2

$\huge {\red{\boxed{ \overline{ \underline{ \mid\mathfrak{\blue{An}}{\mathrm{\pink{sw}}{ \sf{\green{er}}} \gray{\colon}\mid}}}}}}$

Given :

• Length (L) = 2x² - 3x m
• Breadth (B) = x + 10 m

____________________________

To Find :

• Degree of Polynomial of Area.
• Perimeter and area for f(5)

____________________________

Solution :

Formula for Perimeter of Rectangle is :

$\large {\boxed{\sf{Perimeter \: = \: 2(L \: + \: B) }}} \\ \\ \implies {\sf{Perimeter \: = \: 2(2x^2 \: - \: 3 \: + \: x \: + \: 10)}} \\ \\ \implies {\sf{Perimeter \: = \: 2(2x^2 \: + \: x \: + \: 7)}} \\ \\ \implies {\sf{Perimeter \: = \: 4x^2 \: + \:x \: + \: 7}}$

Here Degree of Polynomial is 2 as the highest degree is 2.

___________________________________

As we know that,

Length = f(x) = 2x² - 3

Put x = 5

⇒Length = 2(5)² - 3

⇒Length = 2(25) - 3

⇒Length = 50 - 3

⇒Length = 47

___________________

Similarly, Breadth = f(x) = x + 10

Put x = 5

⇒Breadth = 5 + 10

⇒Breadth = 15 m

___________________________

Now, Formula for Perimeter is :

$\large {\boxed{\sf{Perimeter \: = \: 2(L \: + \: B) }}} \\ \\ \implies {\sf{Perimeter \: = \: 2(47 \: + \: 15)}} \\ \\ \implies {\sf{Perimeter \: = \: 2(62)}} \\ \\ \implies {\sf{Perimeter \: = \: 124 \: m}}$

And formula for Area is :

$\large {\boxed{\sf{Area \: = \: L \: \times \: B}}} \\ \\ \implies {\sf{Area \: = \: 47 \: \times \: 15}} \\ \\ \implies {\sf{Area \: = \: 705 \: m^2}}$

So, Perimeter and Area are 124 m, 705 m² respectively