A $1.5 m$ wide footpath runs all along the fence outside a park $40 m$ long and $30 m$ wide. What is the perimeter of the fence and what is the area of the footpath?

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Solution

As two dimensions of the park are given, it can be assumed to be a rectangle in shape.
Perimeter of rectangular fence $= 2 (l e n g t h + b r e a d t h) = 2 (40 + 30) m = 140 m$
Length of the outer rectangle (path + park) $= 40 + 1.5 + 1.5 = 43 m$
Breadth of the outer rectangle (path + park) $= 30 + 1.5 + 1.5 = 33 m$
Area of outer rectangle PQRS $= l e n g t h \times b r e a d t h = 43 \times 33 = 1419 m^{2}$
Area of the park ABCD $= 40 \times 30 = 1200 m^{2}$
$∴$ Area of the footpath $=$ Area of outer rectangle $-$ Area of park $= 1419 - 1200 = 219 m^{2}$

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A 1.5 m wide footpath runs all along the fence outside a park 40 m long and 30 m wide. What is the perimeter of the fence and what is the area of the footpath?

A $1.5 m$ wide footpath runs all along the fence outside a park $40 m$ long and $30 m$ wide. What is the perimeter of the fence and what is the area of the footpath?