Question

there is a 2.5 meter wide path around the square shapedgarden of sumana . the area of the path is 165sq meter . calculate the area of garden and length of diagonal
mark u brainliest .. help step by step

Answer 1

Answer:

Area of the Garden is 169 meter-square

Diagonal of the square is 18.38 meter.

Step-by-step explanation:

You have to understand the concept :

the garden is a square and there is a path surrounding the square garden.

so , the resulting figure ( square garden and path ) also becomes a square , whose side is x+ 2.5+2.5 .

Don't make the mistake of writing the side of the bigger square as only x+2.5 , it'll be wrong. You have to consider both ends of the square garden .

Now , Area of the big square - Area of the small square is equal to the area of the path(=165)

so, (x+5)(x+5) - (x)(x) = 165 .

Solve this to get the value of x (=13).

So , area of the square garden= (x)(x) = 13×13 = 169 meter square.

Diagonal of the Square garden = 1.414×13 = 18.38m

(diagonal of a square of side 'a' = √2a)

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=

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

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