Question

Area of a rectangular garden is 8000 sq.mts. Ratio in length and breadth is 5:4. A path of uniform width, runs all round the right inside of the garden. If the path occupies 3200m^2, What is its width?​

Answer 1

x can't be 80 because
100-2x
100-160
-60 the length is can't be negative.

Answer 2

Answer:

10 m

Step-by-step explanation:

Given, 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' metres.

⇒ 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.

∴ Width = 10 m.

Hope it helps!