Question

The area of rectangular is (15x²y+20xy)sq unit and its breadth is 5xy unit. find its length and perimeter​

Answer 1

Answer:

see explanation

Step-by-step explanation:

The area (A) of a rectangle is calculated as

A = length × breadth

given A = 15x²y + 20xy and breadth = 5xy , then

15x²y + 20xy = length × 5xy ( divide both sides by 5xy )

$\frac{15x^2y+20xy}{5xy}$ = length ( simplify left side )

$\frac{15x^2y}{5xy}$ + $\frac{20xy}{5xy}$ = length , then

length = 3x + 4 units

The perimeter (P) of a rectangle is calculated as

P = 2( length + breadth )

   = 2(3x + 4 + 5xy ) ← distribute parenthesis

   = 6x + 8 +10xy

That is

length = 3x + 4 units and perimeter = 10xy + 6x + 8 units

Answer 2

Answer:

$\sf \textsf{Length} = 3x + 4$

$\sf \textsf{Perimeter} = 6x + 10xy + 8$

Step-by-step explanation:

To find the length of the rectangle, we can use the formula for the area of a rectangle:

$\Large\boxed{\boxed{\sf \textsf{Area} = \textsf{Length} \times \textsf{Breadth}}}$

Given that the area of the rectangle is $\sf 15x^2y + 20xy$ square units and the breadth is $\sf 5xy$ units, we can set up the equation:

$\sf 15x^2y + 20xy = \textsf{Length} \times 5xy$

$\sf \textsf{Length} = \dfrac{15x^2y + 20xy}{5xy}$

$\sf \textsf{Length} = \dfrac{5xy(3x + 4)}{5xy}$

$\sf \textsf{Length} = 3x + 4$

So, the length of the rectangle is $\sf 3x + 4$.

To find the perimeter of the rectangle, we use the formula for the perimeter of a rectangle:

$\Large\boxed{\boxed{\sf \textsf{Perimeter} = 2(\textsf{Length} + \textsf{Breadth})}}$

Substituting the given values:

$\sf \textsf{Perimeter} = 2((3x + 4) + 5xy)$

$\sf \textsf{Perimeter} = 2(3x + 4 + 5xy)$

$\sf \textsf{Perimeter} = 2(3x + 5xy + 4)$

$\sf \textsf{Perimeter} = 2(3x + 5xy) + 2(4)$

$\sf \textsf{Perimeter} = 6x + 10xy + 8$

So, the perimeter of the rectangle is $\sf 6x + 10xy + 8$.