Perimeter = Distance covered in 8 min. =  \(\left(\frac{12000}{60}\times8\right)\)  = 1600m.

Let length = 3x metres and breadth = 2x metres.

Then, 2(3x + 2x) = 1600 or x = 160.

So, Length = 480 m and Breadth = 320 m.

So, Area = (480 x 320) m² = 153600 m².

100 cm is read as 102 cm.

So, A₁ = (100 x 100) cm² and A₂ (102 x 102) cm².

(A₂ - A₁) = [(102)² - (100)²]

= (102 + 100) x (102 - 100)

= 404 cm²

^So, Percentage error =   \(\left(\frac{404}{100\times100}\times100\right)\) % = 4.04%

\(\frac{2(l+b)}{b}=\frac{5}{1}\)

2l + 2b = 5b

 3b = 2l

b=  \(\frac{2}{3}l\)

Then, Area = 216 cm²

 l x b = 216

\(l\times\frac{2}{3}l=216\)

l² = 324

 l = 18 cm.

Let original length = x metres and original breadth = y metres.

Original area = (xy) m².

New length = \(\left(\frac{120}{100}x\right)m=\left(\frac{6}{5}x\right)m.\)

New breadth =  \(\left(\frac{120}{100}y\right)m=\left(\frac{6}{5}y\right)m.\)

New Area = \(\left(\frac{6}{5}x\times\frac{6}{5}y\right)m^{2}.=\left(\frac{36}{25}xy\right)m^{2}\)

The difference between the original area = xy and new-area 36/25 xy is

= (36/25)xy - xy

= xy(36/25 - 1)

= xy(11/25) or (11/25)xy

So, Increase % =    \(\left(\frac{11}{25}xy\times\frac{1}{xy}\times100\right)\)  %= 44%

Area of the park = (60 x 40) m² = 2400 m².

Area of the lawn = 2109 m².

 Area of the crossroads = (2400 - 2109) m² = 291 m².

Let the width of the road be x metres. Then,

60x + 40x - x² = 291

 x² - 100x + 291 = 0

 (x - 97)(x - 3) = 0

 x = 3.

Other side  =  \(\sqrt{\left(\frac{15}{2}\right)^{2}-\left(\frac{9}{2} \right)^{2}ft}\)

= \(\sqrt{\frac{225}{4}-\frac{81}{4}ft}\)

= \(\sqrt{\frac{144}{4} ft}\)

6.ft.

So, Area of closet = (6 x 4.5) sq. ft = 27 sq. ft.

Let original length = x and original breadth = y.

Decrease in area =  \(xy-\left(\frac{80}{100}x\times\frac{90}{100}y\right)\)

= \(\left(xy-\frac{18}{25}xy\right)\)

= \(\frac{7}{25}xy\)

So, Decrease %  =    \(\left(\frac{7}{25}xy\times\frac{1}{xy}\times100\right)\)   % =  28%

Let the side of the square(ABCD) be x metres.

Then, AB + BC = 2x metres.

\(AC = \sqrt{2x}=(1.41x)m.\)

Saving on 2x metres = (0.59x) m.

Saving % =    \(\left(\frac{0.59}{2x}\times100\right)\)  % = 30% (approx.)

\(\sqrt{l^{2}+b^{2}}\)

Also, lb = 20.

(l + b)² = (l² + b²) + 2lb = 41 + 40 = 81

 (l + b) = 9.

 Perimeter = 2(l + b) = 18 cm.