Question

4.there is a rectangular garden whose length and width are 60m x 20m.there is a walkway of uniform width around garden. area of walkway is 516m^2. find width of walkway

Answer 1

There is a rectangular garden whose length and width are 60 m x 20 m.

There is a walkway of uniform width around garden.

Refer to the attached image.

Let the uniform width around the garden be 'x' meters.

Since, area of walkway = 516 square meters

Since, area of rectangle = length x width

(AB $\times$ CB)- area of garden = 516

[(60+2x)  (20+2x) ] - (60 x 20)= 516

1200+ 120x + 40x + 4$x^2$ -1200= 516

4$x^2$ + 160x-516 = 0

$x^2+40x-129=0$

$x^2+43x-3x-129=0$

$x(x+43)-3(x+43)=0$

(x+43)(x-3)=0

Therefore, x = -43 and x = 3

Width can'not be negative.

Therefore, the width of the walkway is 3 meters.

Answer 2

The options for this question are missing:

These are the options:

i.1

ii.2

iii.3

iv.4

Answer:

Area of Garden = 60*20 = 1200 sq m.

Total Area of garden and walkway = 1200+516= 1716 sq m.

Let assume width of walk way be x

So (60+2x)(20+2x) = 1716

Or x = 3, -43

3 is correct answer

Since 3 is positive.

Solution 2:

Area of Garden = 60*20 = 1200 sq m.

Total Area of garden and walkway = 1200+516= 1716sq m.

Let us assume that width of the walk way be x

therefore(60+2x)(20+2x) = 1716

x = 3, -43

since width can't be negative