Question

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There is a 2.5m wide path around the rectangular garden of shiraj's. The area path is 165sq.meter.let us calculate the area of garden and the length of diagonal​

Answer 1

Step-by-step explanation:

Length of the garden

= L - 2 × width of path

= L – 2(2.5) = (L – 5)

Breadth of the garden

= B - 2 × width of path

= B – 5

We know, area of square = length × breadth

Area of the garden = (L - 5)(B - 5)

Total Area = L × B

Area of path = Total Area – Area of garden = 165

LB - (L - 5)(B - 5) = 165

⇒ LB – LB + 5L + 5B - 25

⇒ 5B + 5L - 25 = 165

⇒ 5(L + B) = 190

⇒ L + B = 38m

Let L = 20m

B = 18m

Area of the garden = (20 - 5)(18 - 5) = 195m2

We know, diagonal of a rectangle

Where, L = length of rectangle and B = breadth of rectangle

Length of the Diagonal =27

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Answer 2

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The area of the lawn = (14)² or 196 m² and Length of diagonal=14 $\sqrt{2}.$

Step-by-step explanation:

Step-by-step explanation:

let the side of the garden be x

Given width of the path = 2.5m

Side of the garden including path = x + 2(2.5m) = x + 5m

So, area of garden = (Area of the garden including the path) - (Area of the path)

Area of a square = (side)²

Therefore, we say :

x² = (x + 5)² – 165

x² = (x² + 10x +25) - 165

x² = x²+ 10x + 25 - 165

x² = x² + 10x - 140

x² - 140 = x² - 10x

x² - x² - 140 = -10x

-140 = -10x

140 = 10x

Therefore x = 140/10 = 14

the side of the garden = 14 m

The area of the garden = (14)² or 196 m².

Length of diagonal=

$\sqrt{2} \times side \: of \: square$

$= \sqrt{2} \times 14 \\ = 14 \sqrt{2}$