Answer:
[tex]length=(\sqrt{40} )m,breadth=\frac{4\sqrt{40} }{5} m[/tex]
Step-by-step explanation:
- So the ratio 4:5 relates the length and breadth
- Now the length is always longer that the breadth so 5 represents the length and 4 the breadth
- A ratio can be written as a fraction so [tex]4:5=\frac{4}{5}[/tex]
- Let [tex]l[/tex] mean length and [tex]b[/tex] breadth, so the ratio [tex]b:l=4:5,so,b:l=\frac{b}{l}=\frac{4}{5}[/tex]
- So if [tex]\frac{b}{l}=\frac{4}{5}[/tex] then multiply both sides by [tex]l[/tex] and you get [tex]b=\frac{4}{5} l[/tex]
- Now the equation for area is [tex]area=length*breadth[/tex] or [tex]A=l*b[/tex]
- Since our breadth [tex]b[/tex] equals [tex]\frac{4}{5} l[/tex] then we substitute for the breadth
- So [tex]A=l*(\frac{4}{5}*l)=\frac{4}{5}*l*l=\frac{4}{5} l^2[/tex] so [tex]A=\frac{4l^{2}}{5}[/tex]
- We know the Area is [tex]32m^2[/tex] so [tex]32m^2=\frac{4l^{2}}{5}[/tex] so we simplify
- [tex]5*(32m^2)=5*(\frac{4*l^{2}}{5})\\ 160m^2=4*l^2\\ \frac{160m^{2}}{4}=\frac{4*l^{2}}{4} \\ 40m^2=l^2\\ l^2=40m^2\\ \sqrt{l^{2}} =\sqrt{40m^{2}} \\ l=(\sqrt{40})m[/tex]
- Now we find the breadth, since
- [tex]b=\frac{4}{5}*l \\ b=\frac{4}{5}*(\sqrt{40} )m\\ b=\frac{4\sqrt{40} }{5} m[/tex]
