Question

the length and bredth of a rectangular park are in ratio 8:5.A path 1.5 m wide ,running all around the outside of the park has an area of 594m Find the dimensions of the park
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Answer 1

Given :-

The length and breadth of a rectangular park are in ratio 8:5.

A path 1.5 m wide running all around the outside of the park has an area of 594 m².

To find :-

The dimensions of the park.

Solution :-

Given that

The ratio of the length and breadth of a rectangular park = 8:5

Let they be 8X m and 5X m

The length of the park (l) = 8X m

The breadth of the park (b) = 5X m

We know that

Area of a rectangle = length×breadth sq.units

Area of the rectangular park

= 8X×5X m²

= 40X² m² ------------(1)

The width of the path running outside the park

(w) = 1.5 m

Length of the outer rectangle = l+2w

= 8X+2(1.5) m

= 8X+3 m

Breadth of the outer rectangle = b+2w

= 5X+2(1.5) m

= 5X+3 m

Area of the outer rectangle

= length × breadth

= (8X+3)(5X+3) m²

= 8X(5X+3)+3(5X+3)

= 40X²+24X+15X+9

= 40X²+39X+9 m² ---------(2)

We have,

Area of the Path = 594 m²

Area of the path = Area of the outer rectangle - Area of the inner rectangle

=> 594 = 40X²+39X+9-40X²

=> 594 = 39X+9

=> 39X+9 = 594

=> 39X = 594-9

=> 39X = 585

=> X = 585/39

=> X = 15 m

Now,

If X = 15 m then the length

= 8X

= 8(15)

= 120 m

If X = 15 m then the breadth

= 5X

= 5(15)

= 75 m

Alternative Method:-

Length = 8X m

Breadth = 5X m

Width of the path = 1.5 m

Area of the path = 594 m²

Area of the a path = 2w(l+b+2w) sq.units

=> 2(1.5)(8X+5X+2×1.5) = 594

=> 3(13X+3) = 594

=> 13X+3 = 594/3

=> 13X+3 = 198

=> 13X = 198-3

=> 13X = 195

=> X = 195/13

=> X = 15 m

Now,

If X = 15 m then the length

= 8X

= 8(15)

= 120 m

If X = 15 m then the breadth

= 5X

= 5(15)

= 75 m

Answer :-

The dimensions of the rectangular park are 120 m and 75 m

Used formulae:-

• Area of a rectangle = length×breadth sq.units

• l and b are the dimensions of a rectangle and a path with w units running outside around the rectangle then the area of the path = 2w(l+b+2w) sq.units

Answer 2

Step-by-step explanation:

Given :-

The length and breadth of a rectangular park are in ratio 8:5.

A path 1.5 m wide running all around the outside of the park has an area of 594 m².

To find :-

The dimensions of the park.

Solution :-

Given that

The ratio of the length and breadth of a rectangular park = 8:5

Let they be 8X m and 5X m

The length of the park (l) = 8X m

The breadth of the park (b) = 5X m

We know that

Area of a rectangle = length×breadth sq.units

Area of the rectangular park

= 8X×5X m²

= 40X² m² ------------(1)

The width of the path running outside the park

(w) = 1.5 m

Length of the outer rectangle = l+2w

= 8X+2(1.5) m

= 8X+3 m

Breadth of the outer rectangle = b+2w

= 5X+2(1.5) m

= 5X+3 m

Area of the outer rectangle

= length × breadth

= (8X+3)(5X+3) m²

= 8X(5X+3)+3(5X+3)

= 40X²+24X+15X+9

= 40X²+39X+9 m² ---------(2)

We have,

Area of the Path = 594 m²

Area of the path = Area of the outer rectangle - Area of the inner rectangle

=> 594 = 40X²+39X+9-40X²

=> 594 = 39X+9

=> 39X+9 = 594

=> 39X = 594-9

=> 39X = 585

=> X = 585/39

=> X = 15 m

Now,

If X = 15 m then the length

= 8X

= 8(15)

= 120 m

If X = 15 m then the breadth

= 5X

= 5(15)

= 75 m

• thanks