Question

3. The dimensions of a rectangular field are (4x+y) metre and (3x-y) metre. Find its area.​

Answer 1

Answer:

• The area of the rectangular field is 12x² - y² - xy.

Step-by-step explanation:

Given that:

• Length of the rectangular field  = (4x + y)
• Breadth of the rectangular field = (3x - y)

To Find:

• Area of the rectangular field.

As we know that:

• Area of a rectangle = (l × b) sq. units

Where,

• l = Length of the rectangle
• b = Breadth of the rectangle

Substituting the values,

Area of rectangular field = (4x + y)(3x - y)

Multiplying the values,

$\sf{\longmapsto4x(3x-y)+y(3x-y)}$

$\sf{\longmapsto12x^2-4xy+3xy-y^2}$

$\sf{\longmapsto12x^2-xy-y^2}$

$\sf{\longmapsto12x^2-y^2-xy}$

Hence, the area of the rectangular field is 12x² - y² - xy

More formulas:

• Perimeter of a rectangle = 2(l + b) units

• $\rm{Diagonal \;of\;a\;rectangle=\sqrt{l^2+b^2}\;units}$

Properties of rectangle:

• The opposite sides are parallel and equal to each other.
• Each interior angle is equal to 90°.
• The sum of all the interior angles is equal to 360°.
• The diagonals of rectangle bisect each other.
• Both the diagonals have the same length.

Answer 2

the area of the rectangle =12×Sq