Question

a path of uniform width runs round the inside a rectangular field of 38 metre long and 32 metre wide. if the path occupies 600m². find the width.

No spamming​

Answer 1

Answer:

area of path =(l+b−2x)2x=600

take help from options to save your valuable time take option (b) x = 5m

(38+32+2×5)2×5

=(70−10)×10=60×10=600

Answer 2

AnswEr :

5 m.

$\bf{\pink{\underline{\underline{\bf{Given\::}}}}}$

A path of uniform width run round the inside a rectangular field of 38 m long and 32 m wide. If the path occupies 600 m².

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(11.1,2){\large{(38+2r)m}}\put(9,0.7){\large{(32+2r)m}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(8.4,2){\large{38m}}\put(9.2,1.4){\large{32m}}\put(8,1.26){\line(1,0){2.7}}\put(8.3,1){\line(0,2){1.76}}\put(10.7,1.25){\line(0,3){1.5}}\put(8.3,2.74){\line(3,0){2.4}}\put(8.1,1.07){\scriptsize{r}}\end{picture}$

$\bf{\pink{\underline{\underline{\bf{To\:find\::}}}}}$

The width.

$\bf{\pink{\underline{\underline{\bf{Explanation\::}}}}}$

$\star\:{\sf{Let\:the\:width\:of\:the\:path\:be\:r}}$

$\bf{We\:have}\begin{cases}\sf{Outside\:of\:length\:of\:field=38+r+r=(38-2r)m}\\ \sf{Outside\:of\:breadth\:of\:field=32+r+r=(32-2r)m}\end{cases}}$

$\blacksquare\:\bf{\underline{\underline{\tt{Accordig\:to\:the\:question\::}}}}}$

$\mapsto\tt{Area\:of\:path=(Outer\:area)-(Inner\:area)}\\\\\mapsto\tt{600=(38-2r)(32-2r)-(38\times 32)}\\\\\mapsto\tt{600=1216-76r-64r+4r^{2} -1216}\\\\\mapsto\tt{600=\cancel{1216}-140r+4r^{2} \cancel{-1216}}\\\\\mapsto\tt{600=-140r+4r^{2} }\\\\\mapsto\tt{600=4(-35r+r^{2} )}\\\\\mapsto\tt{\cancel{\dfrac{600}{4} }=-35r+r^{2} }\\\\\mapsto\tt{150=-35r+r^{2} }\\\\\mapsto\tt{r^{2} -35r+150=0}\\\\\mapsto\tt{r^{2} -30r-5r+150=0}\\\\\mapsto\tt{r(r-30)-5(r-30)=0}\\\\\mapsto\tt{(r-30)(r-5)=0}$

$\mapsto\tt{r-30=0\:\:\:Or\:\:\:r-5=0}\\\\\mapsto\tt{\red{r=30\:\:\:Or\:\:\:r=5}}$

So, we know that r =30 isn't possible according to the question.

Thus,

$\star\:\bf{\large{\orange{\underline{\sf{The\:width\:of\:the\:rectangular\:field\:=r=5\:m.}}}}}$