Question

A play field is 100m by 60m has a footpath all around it on the outside. What is the width of the path if its area be 3/5 of
the area of play field?
24 Tf f() = x2 + 5x + p and g(x) = x2 + 3x + q have a common factor then​

Answer 1

$\text{Let l and b be the length and breadth of the play field}$

$\text{Let w be the width of the footpath}$

$\textbf{Given:}$

$l=100\,m\;\text{and}\;b=60\,m$

$\text{Area of the footpath= \dfrac{3}{5} (Area of the play field)}$

$\textbf{To find:}$

$\text{Width of the footpath}$

$\textbf{Solution:}$

$\text{Area of the footpath}=$

$=\text{Area of the ground}-\text{Area of the play field}$

$=(l+2w)(b+2w)-(l{\times}b)$

$=(100+2w)(60+2w)-(100{\times}60)$

$=6000+200w+120w+4\,w^2-6000$

$=4\,w^2+320\,w$

$\text{But,}$

$\textbf{Area of the footpath}=\bf\dfrac{3}{5}{\times}\textbf{Area of the play field}$

$4\,w^2+320\,w=\dfrac{3}{5}{\times}6000$

$4\,w^2+320\,w=3{\times}1200$

$4\,w^2+320\,w=3600$

$w^2+80\,w=900$

$w^2+80\,w-900=0$

$(w+90)(w-10)=0$

$\implies\,w=-90,10$

$\text{Since w cannot be negative,}\;w=10\;m$

$\textbf{Answer:}$

$\textbf{Width of the footpath is 10 m}$

Find more:

The area of a rectangle is 120m^2. If its length is decreased by 8m and its width is increased by 4m, the area stays the same. Find the perimeter of the original rectangle if all measurements are whole numbers, and show your working. Please answer, much appreciated.

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