Question

. Area of a rectangular garden is 8000 square meters. Ratio in length and breadth is 5:4. A path of uniform width runs all-round the inside of the garden. If the path occupies 3200 m', what is its width?

Answer 1

Answer:

Width = 10 m

Step-by-step explanation:

Given : Area of a rectangular garden is 8000 square meters. Ratio in length and breadth is 5:4. A path of uniform width runs all-round the inside of the garden. If the path occupies 3200 m.

To find : What is its width?

Solution :

Ratio of length and breadth is 5 : 4 and area is 8000 m².

Let length and breadth be 5x and 4x.

∴ Area of rectangle = Length × Breadth

⇒ 8000 = 5x × 4x

⇒ 8000 = 20x²

⇒ x² = 400

⇒ x = 20

Then,

Length = 100 m.

Breadth = 80 m.

Now,

Given that a path runs all round the right inside of the garden.

Let the width of the garden be 'x' meters.

⇒ 8000 - (100 - x - x)(80 - x - x) = 3200

⇒ 8000 - (100 - 2x)(80 - 2x) = 3200

⇒ -(100 - 2x)(80 - 2x) = 3200 - 8000

⇒ (100 - 2x)(80 - 2x) = 4800

⇒ 8000 - 200x - 160x + 4x² = 4800

⇒ 4x² - 360x + 8000 = 4800

⇒ x² - 90x + 800 = 0

⇒ x² - 80x - 10y + 800 = 0

⇒ x(x - 80) - 10(x - 80) = 0

⇒ (x - 10)(x - 80) = 0

⇒ x = 10,80 {It is not possible because breadth is 80 m}

∴ x = 10 m

So, Width = 10 m