Question

Length of a rectangular garden is
10m and its breadth is 8 m if a road of
Uniform width of x m is surrounded
outside the park find the area of the road in terms of x

​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Area of surrounded road = (4x² + 36x) m²

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

First find the area of the rectangular garden

Length of a rectangular garden = 10 m

Breadth of the rectangular garden = 8 m

$\boxed{\bf{Area\:of\:the\:rectangle=Length \times Breadth}}$

Area of the rectangular garden = 10 m * 8 m

= 80 m²

So, Area of rectangular garden = 80 m²

Find Area of the rectangular garden including surrounded uniform width

Road surrounded with uniform width = x m

Length of the rectangular garden including surrounded uniform width = 10 + x + x = (10 + 2x) m

Breadth of the rectangular garden including surrounded uniform width = 8 + x + x = (8 + 2x) m

$\boxed{\bf{Area\:of\:the\:rectangle=Length \times Breadth}}$

Area of the rectangular garden including surrounded uniform width = (10 + 2x) * (8 + 2x)

= 10(8 + 2x) + 2x(8 + 2x)

= 80 + 20x + 16x + 4x²

= (80 + 36x + 4x²) m²

So, Area of the rectangular garden including surrounded uniform width = (80 + 36x + 4x²) m²

Subtract area of rectangular garden from Area of the rectangular garden including surrounded uniform width.

Area of surrounded road = Area of the rectangular garden including surrounded uniform width - Area of the rectangular garden

$\tt{=80 + 36x + 4x^2 - (80)}$

$\tt{=80 + 36x + 4x^2 - 80}$

$\tt{=4x^2 + 36x}$

So, Area of surrounded road = (4x² + 36x) m²

Answer 2

Answer:

here is answer

Step-by-step explanation:

First take out the area and then add x x(10+x+x)=(10+2x)