Question

$\huge\sf{Question}$
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.

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Answer 1

Answer:

Hello Finex!

Your answer is 2m

Step-by-step explanation:

Area of walk =120m^2

Area of EFGH- Area of ABCD=120

$= {x}^{2} + 13x - 30 = 0 \\ \\ x = 2 \: or \: - 15$

As -15 can't be the width of walk so it is 2

$\therefore \: x = 2m$

Length of outer rectangle =16+(2*2)=20m

Breadth " " " =10+(2*2)=14m

Hope it helps you from my side

Answer 2

Step-by-step explanation:

Given information

• ⇀ Length of rectangular garden 10m
• ⇀ Breadth of rectangular garden 16m
• ⇀ The area of the walk is 120m²

What we need to calculate

• ⇀ We have to calculate value of x

Assuming

• ⇀ The width of the walk to be x form an equation in x

let's calculate

As we have given the dimensions of the rectangular garden. Hence we'll calculate determine its area by using its formula length × breadth

➜ Area of the rectangular garden = 16m × 10m

➜ Area of rectangular garden = 160m²

We have already given the area of the concrete walk as 120m²

Now, we'll calculate the total area of rectangular garden and the sidewalk

➡️ Total area = Area of rectangular garden + Area of path

➜ Total area = 160 + 120

➜ Total area = 280m²

The uniform width of the sidewalk as X (given in question)

➜The length of the whole rectangle (including concrete path ) =( 16 + 2x )m

➜ The breadth of whole rectangle (including concrete path) = (10 + 2x) m

We'll use these expressions in the total area equation

➜Area of the whole rectangle = length × breadth

• subtracting the value of length and breadth

➜ 280 = (16 + 2x ) (10 + 2x)

• we'll multiply the bracket and simplify the equation

➜ 280 = 4x² + 52x + 160

➜ 0 = 4x² + 52x + 160 - 280

➜ 0 = 4x² + 52x - 120

➜ 0 = 4x² + 52x - 120

• To get the coefficient of x² as 1 ,we will divide the entire equation by 4

➜ 0 = x² + 13x - 30

• split the middle term to get the root of the above quadratic equation

➜ 0 = x² + 15x - 2x - 30

➜0 = x (x + 15) - 2(x + 15)

➜0 = (x - 2 ) (x + 15)

➜ x = 2 or x = -15

❑As the width cannot be negative So, the value of x is 2

length of outer Rectangle

➜ 16 + 2x

➜ 16 + 2×2

➜16 + 4

➜ 20

breadth of outer rectangle

➜10 + 2x

➜10 + 2×2

➜10 + 14

➜14

❑The length of outer rectangle is 20m and breadth of the outer rectangle is 14m